Johnson was National Under-19 champion in 1971 and three times Yorkshire Champion. He was runner-up to Terry Griffiths in the English Amateur championship of 1978 and, with Griffiths being a Welshman, Johnson qualified as England’s representative in that year’s World Amateur in Malta. He gave a very good account of himself and reached the final where he lost to Cliff Wilson. This prompted Johnson to turn professional in 1979.
In Johnson's first season as a professional he was unranked. Johnson turned professional alongside other notable players of the future, including Tony Meo, Mike Hallett and Cliff Wilson. Johnson's first match as a professional came in the non-ranking 1979 Canadian Open. In Round 1 he beat Steve Baruda 5–4. The match included a break of 100, Johnson's first century break as a professional. In the second round Johnson beat John Bear 9–7 and then lost in the last 16 to Kirk Stevens by 9 frames to 2. In the next event, the 1979 UK Championship, Johnson lost his opening match, a last 24 encounter with Bill Werbeniuk by 9 frames to 3. At the 1980 British Gold Cup, Johnson had Willie Thorne and Ray Edmonds in his qualifying group. Johnson lost 3–0 to Thorne but beat Edmonds 2–1, which was not enough for Johnson to qualify out of his group. At the 1980 World Championship Johnson beat Roy Andrewartha 9–5 in Round 1 and progressed to the last 48 where Johnson lost 9–6 to Pat Houlihan. Johson won just £100 in his first professional season, received no ranking points and he finished the season unranked.
Johnson was unranked throughout the 1980/1981 season. His season started with the 1980 UK Championship in which he beat John Dunning 9–6 in the last 32 before losing 9–4 in the last 24 to Patsy Fagan. At the 1981 Yamaha Organs Trophy Johnson lost all three of his qualifying round matches; he was beaten 3–0 by both Mike Hallett and Tony Knowles and 2–1 by Willie Thorne. The following event however, the 1981 English Professional Championship saw Johnson avenge his loss to Knowles with a comprehensive 9–2 win in the first round. Johnson received a walkover in the last 16 against John Pulman and this took Johnson into the quarter finals, where he lost 9–5 to Ray Edmonds. At the 1981 World Championship Johnson lost his opening match, a last 48 encounter with Tony Meo. Johnson matched Meo virtually frame for frame throughout the match until losing the final frame and the match 9–8. Johnson received no ranking points during the season, his prize money for the season was £850, 28th on the money list and he finished the season still unranked.
Johnson started the season unranked. His first event was the 1981 International Open in which he beat Jim Donnelly 5–4 in Round 1, Murdo Macleod 5–1 in Round 2 and received a walkover against John Pulman in Round 3. In Round 4 Johnson beat Jim Wych 5–3 and then lost in Round 5, the last 32, 5–3 to Graham Miles. In the 1981 UK Championship Johnson began the event with a comprehensive 9–1 win over Tommy Murphy in Round 2. This was followed by a Round 3 9–3 defeat of Mike Watterson and in Round 4 a 9–4 win over Cliff Wilson. In round 5 Johnson beat the former three-time world champion John Spencer 9–5 and this earned Johnson a last 16 appearance at the UK Championship against another former world champion, Ray Reardon, to whom Johnson narrowly lost 9–7. At the 1982 International Masters, Johnson began the event in the pre-qualifying group stage with a 2–1 loss against Dave Martin, and 2–0 wins over both Geoff Foulds and Cliff Wilson. The results were enough to take Johnson into the next qualifying round where he lost 2–1 to John Virgo, but beat John Spencer 2–1 and Dave Martin (again) 2–0. In the third and final group stage Johnson lost 2–0 to Dennis Taylor and Reardon but beat Virgo 2–1, but the win was not enough to take Johnson out of the group stage. In Round 1 of the 1982 World Championship Johnson beat Vic Harris 9–4 and reached the last 48, where he lost 9–8. After a 2–0 Round 1 defeat by Jackie Rea in the 1982 Bass and Golden Leisure Classic Johnson ended the season with no ranking points, £2,950 prize money – 25th in the money list, but was again unranked.
Johnson started the season unranked and in his first match he received a walkover against John Phillips in Round 1 of the 1982 International Open. Johnson lost his last 48 match against Cliff Wilson 5–4. In the last 32 of the 1982 Professional Players Tournament Johnson began with a solid 5–1 last 64 win against Graham Miles and a last 32 5–1 win against Kirk Stevens. Johnson followed this up with a 5–4 last 16 win over Mark Wildman and in the quarter final Johnson was beaten 5–1 by John Virgo, a result which earned Johnson his first ranking points. Johnson started the 1982 UK championship with a narrow 9–8 victory over Vic Harris in the last 48 before being comprehensively beaten 9–1 by Terry Griffiths in the last 32. At the 1983 International Masters, Johnson again started in pre-qualifying and he scored 2–0 victories over Murdo Macleod and Mario Morra, but lost his following two matches 2–0 to Willie Thorne and Tony Meo. In qualifying for the 1983 World Championship Johnson scored a 10–0 whitewash over Paul Watchorn in Round 1 but lost 9–8 to Cliff Wilson and thus failed to reach the main event at the Crucible Theatre. Johnson won £4,650 in prize money over the season and received 2 ranking points
Johnson's wins in the previous season had provided him with his first ranking points and they were enough for him to be ranked 23rd in the world. In the last 48 of the 1983 International Open Johnson beat Dennis Hughes 5–1 and then lost 5–2 to Eddie Charlton in the last 32. Johnson began the untelevised 1983 Professional Players Tournament in fine form with an opening frame 117 break in a last 64 5–3 win over Pascal Burke. In the last 32 Johnson beat a young up and coming Jimmy White 5–3 to set up a rematch against Eddie Charlton, which this time Johnson won 5–0 and included a 111 break. In the quarter final Johnson beat the highly ranked Cliff Thorburn 5–1 and in the semi final Johnson beat Tony Meo 9–6 in order to reach his first major final against Tony Knowles. 1–6 down to Tony Knowles at one stage, Johnson fought back to take the match to a decider, and losing 9–8. At the 1983 UK Championship Johnson beat Matt Gibson 9–6. In the last 32 Johnson made a 119 break on his way to beating John Virgo 9–6 in the last 32. In the last 16 Johnson beat David Taylor 9–3 to earn himself another quarter final appearance where he lost 9–2 to Terry Griffiths. At the 1984 Classic Johnson beat Frank Jonik 5–2 in the last 48 before losing 5–4 to John Spencer in the last 32. At the 1984 International Masters Johnson lost 2–0 to Colin Roscoe and Doug French in the qualifying group stage. In qualifying for the 1984 World Championship Johnson won his first match, a last 48 encounter with Matt Gibson 10–3 and this earned Johnson made his debut at the Crucible stage of the 1984 World Snooker Championship, where he was beaten 10–1 by Dennis Taylor. Johnson ended the season with prize money of £12,900 the 18th highest for the season and 4 ranking points.
Johnson started the 1984/85 season ranked 19th in the World. At the 1984 Costa Del Sol Classic Johnson made a 105 break in his 3–1 quarter final win over Mick Fisher and then lost 3–2 in the semi final to Dennis Taylor. At the 1984 International Open Ranking event, Johnson beat Mario Morra 5–0 in the last 48 and Eddie Charlton 5–1 in the last 32 before losing again to Dennis Taylor, this time 5–2 in the last 16. In the following ranking event, the 1984 Grand Prix Johnson beat Paul Medati 5–1 in the last 64 but then lost 5–4 to Ian Williamson last 32. At the 1984 UK Championship Johnson beat John Rea 9–6 in the last 48 and John Spencer by the same scoreline in the last 32. In the last 16 Kirk Stevens beat Johnson 9–2. In the 1985 Mercantile Credit ranking event Johnson reached the semi-final with a last 48 5–4 win over Ray Edmonds, a 5–1 last 32 win over Tony Knowles and a 5–0 whitewash of Cliff Wilson in the last 16 and a 5–1 win over Warren King in the quarter final. In the semi-final Johnson met Cliff Thorburn and apart from a single century from Thorburn, Johnson lost the low scoring match by 9 frames to 2. 1985 English Professional Championship – Professional Non-ranking Last 16 John Virgo 9 (17) 4 Joe Johnson Last 32 Joe Johnson 9 (17) 1 George Scott 1985 British Open – Professional Ranking Last 64 Wayne Jones 6 (11) 5 Joe Johnson 1985 World Championship – Professional Ranking Last 32 Bill Werbeniuk 10 (19) 8 Joe Johnson Last 48 Joe Johnson 10 (19) 6 Geoff Foulds and although Johnson was beaten 10–8 at the 1985 World Championship by Bill Werbeniuk the results were enough to raise Johnson's ranking for the following season.
Johnson began the season inside the top 16 for the first time in his career, albeit only just at World number 16. When Johnson lost 5–3 to Cliff Thorburn in the first round of the 1986 Masters, people started to say that he could not perform in front of the TV cameras. At the 1986 World Championship Johnson was relatively unheralded, especially as he'd never won a televised match until just the previous year. He had also never won a match at the Crucible Theatre, and was rated a 150–1 outsider. He beat former champion Terry Griffiths 13–12 in the quarter-finals after trailing 12–9. The match was particularly noteworthy, from leading 9–7 going into the final session, Griffiths then won five frames to lead 12–9 before Johnson won 4 straight frames including two century breaks to win 13–12. and then defeated Knowles 16–8 in the semi-finals. In the final he met world number 1 Steve Davis – then at the peak of his ability. Johnson trailed 3–1 and 7–4 in the opening stages but surged ahead to lead 12–8 and ended the third session 13–11 ahead. In the evening session Johnson took five of the opening six frames to seal a shock 18–12 victory. A supporter of Bradford City football club, he wore a T-shirt with the slogan "Bradford's Bouncing Back" (a reference to the Bradford City stadium fire a year earlier) whenever he was not playing during the tournament.
Johnson had a poor season as world champion, reaching only one semi-final. By his own admission, he arrived at the Crucible for the 1987 World Championship hoping merely to progress past the first round. However, he defied expectations and reached the final again, en route edging out a young Stephen Hendry 13–12 in a close quarter-final. Once again his opponent in the final was Davis, but this time Johnson was beaten 18–14. He reached number 5 in the world rankings in the 1987–88 season, largely as a result of his performances at the Crucible. Johnson remains the player who came closest to beating the "Crucible Curse", in that no first-time world champion has ever successfully defended the title. Johnson's defence saw him both reach the final and come within four frames of victory. Ken Doherty also reached the final in 1998, a year after his first win at the Crucible, but lost by a greater margin to John Higgins. No other first-time champion has reached the final the following year.
Johnson won the Langs Scottish Masters in 1987, beating Terry Griffiths 9–7 in the final and taking his only other major snooker title. He reached the semi-finals of the 1987 UK Championship and came close to making a maximum break against Jimmy White, but missed the pink on 134 and went on to lose the match 4–9. He reached the semi-final of the 1988 Masters.
During the season Johnson was ranked 11th in the World.
Johnson lost 10–8 to Darren Morgan in the opening round of the 1990 World Championship. He finished the 1989/90 season ranked number 11, thus ending the decade ranked inside the top 16.
Johnson started the season outside of the top 16 ranked No.18 in the World. The first ranking event of the season saw Johnson lose to Colin Roscoe in the last 64 of the 1990 Grand Prix and this was followed last 64 defeats to James Wattana in the 1990 Asiain Open and Jim Wych in the 1990 Dubai Classic, . In the 1990 UK Championship Johnson narrowly beat Warren King 9–8 in the last 64 and followed that with a 9–5 victory over Gary Natale in the last 32 before losing to John Parrot 9–8 in the last 16. In the following ranking event, the 1991 Classic Johnson beat Paddy Browne in the last 64 and a 5–0 win over John Campbell took Johnson into the last 16 where he lost 5–3 to Rod Lawler. A last 64 win against Chris Cookson in the 1991 British Open took Johnson to the last 32 where he lost to Mike Hallet. In 1991 European Open Johnson beat Andrew Cairns to set up another last 32 appearance where he 5–0 to Stephen Hendry. A 10–8 victory over Nigel Bond saw Johnson qualify for his last appearance at the Crucible in the World Championship where he lost 10–6 in the last 32 to Dennis Taylor.
Johnson started the season as World number 26. In the first ranking event of the season, 1991 Dubai Classic, Johnson beat Andy Hicks in the last 64 and Brady Gollan in the last 32 to set up a last 16 match against Peter Francisco where he lost 5–4. Johnson went one better in the following ranking even, the 1991 Grand Prix, when he beat Warren King in the last 64, Tony Jones in the last 32 and Mike Hallett in the last 16 to set up a quarter final against Nigel Bond where he lost 5–3. Johnson withdrew from the 1991 Benson and Hedges Satellite Championship and Neil Martin received a Walkover in their last 64 match. In the 1991 UK championship Johnson lost first round last 64 match to Darren Morgan. Johnson lost both of his first round last 64 matches in the following ranking events, the 1992 Classic to Paul McPhillips, to Tony Meo in the 1992 Asian Open . In the following ranking event, the 1992 Welsh Open, Johnson's season improved when he beat Paul McPhillips in the last 64 and Tony Knowles in last 32 to set up a last 16 match against Steve James who whitewashed him 5–0. Johnson reached the last 16 again in the following tournament, the 1992 British Open, when he beat Joe Grech in the last 64, Nigel Bond in the last 32 before losing to Alain Robidoux in the last 16. the 1992 Strachan Open Johnson reached the last 32 and in the penultimate ranking even before the World Championship, the 1992 European Open, Johnson beat Alan McManus 5–1 in the last 64 before losing to 5–2 to Stephen Hendry in the last 32. Johnson narrowly missed out on qualifying for the 1992 World Championship after he lost 10–9 to Mick Price in the last 48, Johnson did however make a 141 break during the match – the highest break of the qualifying tournamount.
Johnson's ranking rose to No.23 at the start of the season. The first ranking event of the season saw Johnson beaten 5–2 by Nick Dyson in the last 64 of the 1992 Dubai Classic. At the 1992 Grand Prix Johnson beat Mark Boyd in the last 64 before losing 5–1 to Steve James in the last 32. At the 1992 UK Championship Johnson won the deciding frame to beat Darren Clarke 9–8 before suffering a heavy 9–1 loss to Gary Wilkinson in the last 32. Johnson lost in the last 64 at 1993 Welsh Open to Joe Grech. In the 1993 European Open Johnson beat Anthony Davies in the last 64 and caused an upset by beating John Parrot 5–3 before losing by the same scoreline to Mick Price in the last 16 . At the 1993 British Open Johnson beat Anthony O'Connor 5–2 in the last 64 before losing to Jimmy White in the last 32. John Parrot avenged his earlier defeat to Johnson by beating him in the last 16 of the 1993 Asian Open after Johnson had beaten Martin Clark in the last 32 and Troy Shaw in the last 64 . The penultimate event before the World Championship saw Johnson beaten 5–0 by Billy Snaddon in the last 64 of the 1993 International Open. Needing to win one match to qualify for the World Championship, Johnson lost 10–6 to Karl Payne in the last 48.
Johnon's ranking had dropped to No. 26 for the start of the 1993/94 season. The first ranking event of the season saw Johnson beaten 5–3 by Terry Murphy in the last 48 of the 1993 Dubai Classic. Johnson was beaten by John Higgins in the last 64 of the following event, the 1993 Grand Prix. Having entered the 1993 Benson and Hedges Championship, Johnson lost in the last 128 to Stuart Reardon. Craig Edwards beat Johnson in the last 64 of 1993 UK Championship. The following three events saw Johnson beaten in each of his first round last 64 matches, at the 1993 European Open by Fergal O'Brien, in 1994 Welsh Open by Dave Harold.
Johnson suffered heart and eye problems during the 1990s although he continued to play in qualifying events. In the 1994 UK Championship Johnson was ranked 37th in the World and lost 9–7 to Terry Griffiths in the first round. In the first round of the 1996 UK Championship Johnson overcame Dene O'Kane by a narrow 9–8 scoreline. Johnson then beat Thai Pichit 9–6 in round 2, before losing 9–6 to John Parrott in the last 16. In the 1997 UK Championship Johnson lost in the first round to Quinten Hann. A 5–4 win over Ali Carter in the final qualifying round of the 1997 International Championship took Johnson into the First Round where he comfortably beat Martin Clark 5–1. In Round 2, the last 32, Johnson lost to Parrot. Johnson won the Seniors Pot Black Trophy in 1997, beating Terry Griffiths in the final.
In the 1998 Grand Prix Johnson made the last 32. Johnson lost 5–4 to Steve Judd in Round 5 of the 1998 UK Championship. In the 1999 UK Championship Johnson beat Tony Jones in Round 2 before narrowly losing 9–7 to John Parrot in Round 3.
In the 2000 UK Championship Johnson lost his opening match in Round 3 to Mark Gray. In the 2000 World Championship Johnson beat Somporn Kathawung in Round 4 before losing to Ian McCulloch in Round 5.
Johnson started the season as World No.90. At the 2002 LG Cup Johnson was beat in the Last 128 5–3 by Bob Chaperon and 5–4 in the last 128 of 2002 British Open by Darren Clarke. At the 2002 UK Championship Johnson beat David John 5–3 in the last 128 before losing 5–3 to Rod Lawler. These last 128 defeats then followed: 5–2 against Justin Astley in the 2003 Welsh Open, 5–4 against David McLellan in the 2003 European Open, 5–2 against James Reynolds in the 2003 Irish Masters and 5–0 against Nick Pearce in the 2003 Scottish Open. In the 2003 World Championship however Johnson beat David McLellan 10–5 in the last 128, Simon Bedford 10–6 in the last 96 and Bradley Jones in the last 80 to set up a last 64 match against Ian McCulloch which Johnson only narrowly lost 10–7. Johnson finished the season with £8,650 in prize money and finished the season as World no.96.
Despite being ranked 96th in the World and eligible to play in most of the seasons events, Johnson withdrew from all but two of them. Consequently, the following players received walkovers, 2003 LG Cup Last 128 Supoj Saenla, 2003 British Open Last 128 Alain Robidoux, 2003 UK Championship Last 128 Carlo Giagnacovo, 2004 Welsh Open Last 128 Joe Delaney, 2004 European Open Last 128 Gary Hardiman, 2004 Irish Masters Last 128 Chris Melling. Johnson entered the 2004 Players Championship however where he lost to 5–3 to Stuart Mann in the last 128. Johnson's final event as a professional was the 2004 World Championship where he lost 10–0 to Ian Preece in the last 128. Johnson won just £1,000 during the season and officially finished the season ranked 126th in the World.
Johnson retired in 2005 after breaking his ankle, Johnson was 53 at the time and the then-oldest player on the circuit.
After the revival of the World Seniors event, Johnson was seeded to the quarter finals of the 2010 event where he lost to Steve Davis. In the 2011 event Johnson was seeded into the last 16 where he lost to Parrott and this was followed by similar defeats in Round 1 to Darren Morgan in 2012, Stephen Hendry in 2013 and Paul McPhillips in 2015.
In his spare time Johnson sang in a band (Dresden) claiming to have the best voice among the top players of his era. Johnson was an early influence on, and friend of, the late snooker player Paul Hunter. Johnson has established himself as a regular commentator for Eurosport. In December 2013 John Higgins was quoted as saying in reference to Johnson: "I heard before the tournament [2013 UK Championship] Joe Johnson was slating me. If that guy isn't the worst commentator in the world, he's in the top three". Johnson owns two snooker clubs in West Yorkshire, one in Bradford and one at the Corner Pocket Snooker club Hoyle Mill in Barnsley as well as running three coaching academies. Johnson is married with five sons and two daughters.