Thom began his professional career with Dynamo Berlin. In his time there, he won the GDR Premier League in 1984, 1985, 1986, 1987 and 1988, and the GDR Cup in 1988 and 1989, scoring the only goal of the game in the latter final. In 1988 Thom was the top scorer in East Germany and that same year also voted the East German Footballer of the Year.
On 16 December 1989, Thom became the first East German to sign for a Bundesliga club when he joined West German side Bayer Leverkusen for a transfer fee of 2.5 million Deutsche Mark (approx £900,000). The transfer also placed Thom amongst the highest earners in the Bundesliga and made him the highest paid player at Bayer Leverkusen. Thom made his historic debut for his new club on 17 February 1990, and scored the opening goal in a 3-1 win over FC Homburg. Thom spent over 5 years at Bayer Leverkusen, and picked up a winner's medal on 12 June 1993 win they defeated Hertha BSC II 1-0 in the final of the German Cup.
Thom signed for Glasgow club Celtic in July 1995 for a then club record fee of £2.2million. On 30 November 1997, Thom picked up another winner's medal when he played in the Celtic side that defeated Dundee United 3-0 in the Scottish League Cup Final. Thom moved back to Germany in January 1998 to sign for Hertha Berlin, although his 15 league appearances for Celtic earlier that season saw him pick up a Scottish League championship medal when Celtic clinched the league title in May 1998.
Thom spent four years at Hertha Berlin, before retiring from playing. Thom made his last appearance on 7 March 2001, coming on as a substitute in a 2-1 win over SpVgg Unterhaching. In the 2000-01 season he foremost played in Hertha's reserve team.
Thom played for the East Germany national football team between 1984 and 1990, making 51 appearances and scoring 16 goals. He made his debut in a friendly against Algeria on 10 October 1984. He scored the first of his 16 international goals on 6 February 1985 in another friendly, a 3-2 win over Ecuador. Thom played in six of East Germany's qualifiers for the 1986 FIFA World Cup, and scored his first two competitive goals for his country on 28 September 1985 in a 2-1 win over Yugoslavia in Belgrade. East Germany, however, failed to qualify for the World Cup, finishing third in Group 4 behind France and Bulgaria. He was now a regular in the East German international side, and played in all eight of his nations qualifying ties for Euro 1988. He scored five goals over the campaign, including a hat-trick in a 6-0 away win over Iceland in June 1987. East Germany, however, again failed to qualify; finishing second in the group behind the Soviet Union.
In 1988, Thom took over from goalkeeper René Müller as captain of the national side for six matches, including their first two qualifying games for World Cup against Iceland and Turkey. He scored in both of these World Cup qualifiers, both goals in East Germany's 2-0 win over Iceland and their solitary goal in a 3-1 defeat against Turkey in Istanbul. Thom scored his last goal for East Germany on 8 October 1989 as his side came from a goal down to defeat the Soviet Union 2-1. That left the East Germans needing only a draw away against Austria to qualify for the World Cup. However, they were beaten 3-0 in that game and finished fourth in the qualifying group.
After the reunification of Germany, he played for the unified team in a further 10 matches and scored 2 goals. He made his only appearance in the finals of a major international tournament in 1992 when he came on as a substitute for Stefan Effenberg in the final of Euro 1992 against Denmark (Germany lost 2-0).
After the sacking of Huub Stevens as head coach at Hertha BSC in December 2003, Thom briefly took over for 3 games until Hans Meyer was appointed later that month. Thom became assistant coach at the club and held that position under Meyer's successor, Falko Götz. On 10 April 2007, Thom was sacked along with Götz due to the poor performance of Hertha BSC.
On 15 December 2008 it was announced that Thom would become assistant coach at lower league Holstein Kiel in January 2009. Under head coach Falko Götz, Thom helped Holstein Kiel win promotion from the Regional North League to the national third division in 2009. On 15 February 2010 Holstein Kiel sacked Andreas Thom.
Since the 2010/11 season, Thom has managed the Under-17 team of Hertha BSC.Dynamo Berlin
East German Champion (5): 1984, 1985, 1986, 1987, 1988
East German Cup (2): 1988, 1989
German Cup (1): 1993
Scottish League champion (1): 1998
Scottish League Cup (1): 1997
UEFA European Championship: Runner-up 1992
East German Footballer of the Year (1): 1988