Born in the northern Sydney suburb of Ryde, Tedesco is of Italian descent. He was raised on a hundred hectare property in Menangle in Sydney's south west, complete with his own football field with goal posts. Tedesco played his junior football with the Camden Rams. His father said of his early years, "James couldn't even make the junior rep squad for Wests when he was 14, and from then on he's always sort of scraped in. But once he's made those teams, he's gone on to finish as the best player."
Tedesco was a student of St Gregory's College, Campbelltown, and was in year 7 when Chris Lawrence was studying year 12.
Tedesco played on the wing for the Western Suburbs Magpies in the Harold Matthews Cup competition, with David Nofoaluma at fullback. In 2010, he made the Australian Schoolboys team. "I made the Australian Schoolboys and I learnt to just have confidence in my own ability. I realised it was there – that I had a bit of talent – I just needed the confidence to show it," he said.
Tedesco commenced the 2011 season playing in the S. G. Ball Cup, but was promoted to the Wests Tigers NYC team from round 13. In just his third game he equaled the club record of scoring 4 tries in one match, and went on to be named the team's player of the year.
Attracting the attention of other clubs, Tedesco was the focus of a "bidding war" between the Wests Tigers and St George Illawarra, resulting in the Tigers signing him until the end of 2014. Weeks later, he was named at fullback for the team's first trial-match for the year. However, coach Tim Sheens said he was unlikely to be playing at fullback at the start of the regular season, saying, "'I don't necessarily want to throw that on him at this point. I've got some experienced options."
Having played well in both pre-season trials, Tedesco was named in the starting team to play the Cronulla Sharks in the first game of the season. After showing potential in the early stages of the game, Tedesco suffered an injury to his knee in the 30th minute. The tear to the anterior cruciate ligament in his left knee was the end of his season. Team-mate Benji Marshall said, "Just seeing his reaction in the sheds, he was crying in there and it brought a tear to a few of the boys' eyes as well, because we see him as such a great talent and he's fitted into the squad well and he's a really good kid."
Tedesco returned to first grade in round 4 of the 2013 season, and played on the wing for four weeks. In April, he was chosen to play for NSW City in the annual City vs Country Origin match. Having only appeared in four NRL matches at that time, he was the least experienced player to ever participate in the match. "When they called me up, I thought it was a joke. Even when Brad Fittler got on the phone I didn't think it was real. It was also a problem, because I didn't know whether I was eligible for City or Country," Tedesco said. Tedesco played at fullback in City's 18-12 loss at Coffs Harbour.
With Tim Moltzen moving to halfback before suffering a season-ending injury, Tedesco played most of the rest of the season at fullback, scoring 8 tries in 19 matches. He spent months playing with a cracked fibula, after being advised that he was unlikely to make the injury any worse by playing. Tedesco said the leg was painful when knocked. "It does kill for about five minutes or so, then you run it off and it goes away." At the end of the season, Tedesco was chosen to represent Italy at the 2013 Rugby League World Cup. With Anthony Minichiello captaining and playing at fullback, Tedesco played at right centre for the three games. In his international debut, he scored a try as Italy defeated Wales 32-16.
In February, Tedesco was selected in the Tigers inaugural Auckland Nines squad. On 27 May, he signed a 3-year contract with the Canberra Raiders starting in 2015. A week later, Tedesco back flipped on his deal with the Raiders to stay with the Tigers. During the round 16 clash with the Raiders, Tedesco lasted 15 seconds before he fractured his patella. Tedesco missed the rest of the season. Tedesco said, "“On Twitter Canberra fans would say ‘I hope you break your legs’ and stuff like that and then I play Canberra and it happens. It is a bit weird. It was just a freak accident." Before the end of the year, Tedesco had returned to sprint training and was adjusting his running style to be less "low to the ground". He finished the NRL season with 8 matches and 6 tries.
After an "eye-catching" display in round 2, Tedesco was touted as a possible State of Origin selection. While Tedesco said he felt ready to play in the representative matches, coach Jason Taylor said, "I think that's too early. It was a really good first half and he showed what he can do, but I think that's a bit too early for where he's at."
Between 19 August 2013 and round 7 of the 2015 season, Tedesco had scored 18 tries in 19 appearances. He played in every game of 2015 and was the competition's leader for tackle breaks and the third highest try-scorer. From round 10 onwards, Tedesco ran for over 100 metres in each game, with the fourth highest total in the competition. He was named in the NRL website's Team of the Year and was a finalist for the RLPA's highest honour, the Player's Player.
Tedesco started the 2016 season by scoring 2 tries against the New Zealand Warriors in round 1 and his first career hat-trick against the Manly Warringah Sea Eagles in round 2. He suffered a shoulder injury in round 9, making him unavailable for the City Origin side. At the time of his injury he was the competition's leading try-scorer.
Considered a certainty to play for New South Wales in the first match of the State of Origin series, he was unavailable due to injury, and was not selected for the second when he returned from injury only weeks before. Making his debut in game 3, he ran for 258 metres, the most of any player in the game, as NSW won their only match of the series. It was said he "Showed enough in 80 minutes to suggest the No.1 jersey will be his for many years to come."
With Wests Tigers fighting to make the semis towards the end of the year, Tedesco had his jaw broken in a tackle from Ryan James, ending his season. He recovered to represent the Prime Minister's XIII against Papua New Guinea, but left the field with concussion in the first half. He scored 14 tries in 17 matches with the Tigers. He was named the fullback in the Dally M team of the year.
In March and April, Tedesco alongside Tigers captain Aaron Woods and halves partners Luke Brooks and Mitchell Moses attracted media attention, with speculation about where the players, dubbed as the "Big Four" would end after all of their contracts expired at season’s end. On 3 May, it was announced that Tedesco signed a 4-year contract with the Sydney Roosters, starting in the 2018 season. Tedesco played fullback in all 3 matches in the 2017 State of Origin series, scoring 1 try in game 1 in the 28-4 win at Suncorp Stadium before going down the next 2 matches to lose the shield to Queensland. Tedesco finished his last year with the Wests Tigers with him playing in 21 matches and scoring 5 tries in the 2017 NRL season.
Early in his career, Tedesco studied to be a PE Teacher at the Strathfield campus of Australian Catholic University.