After a long karting career as a child, Stefan stepped up to open-wheel racing in November 2006, competing in the Formula Palmer Audi Autumn Trophy at Snetterton and Brands Hatch. Stefan gradually improved over the course of his first six car races and finished the six-race mini-series in ninth place, also ending as top rookie. He picked up three top-six finishes and set fastest lap in the final round at Brands Hatch. at the Croft round of the 2008 British Formula 3 season. Stefan competed in the 2007 Formula Palmer Audi Championship, the 10th anniversary of the series and also the 10th anniversary of when his brother Justin won the first FPA title. He finished 2nd in the championship after a great final round at Croft, where he scored 2 podiums after his worst qualifying of the season, only starting 7th and 9th for the two races. Stefan overtook a total of 11 cars. He also closed the final gap between him and more experienced driver Tim Bridgman to just 28 points. He scored 4 wins over the course of the season; the first came in round 4 of the championship at the Brands Hatch Grand Prix circuit in front of nearly 50,000 spectators. The second half of Wilson's championship was more successful as he scored 4 pole positions and 3 of his 4 wins. Wilson ended the championship in 2nd place, with a tally of 4 wins, 9 podiums, 4 pole positions, 5 fastest laps, and 2 lap records. At the end of the season he won the McLarenAutosport BRDC Award for young British drivers. Part of the award was a prize drive in a McLaren Formula One car, which took place on the Silverstone National Circuit on 13 November 2009. In 2008 he competed in the British Formula 3 Championship National Class in 2008 with Fluid Motorsport and captured 4 class wins on his way to 4th in the National Class points standings.
Wilson signed to race a partial schedule in Firestone Indy Lights in 2009 for First Motorsports with cars prepared by Walker Racing that included six road and street courses. He qualified third at Long Beach but was sidelined by a mechanical problem towards the finish. His best finish was fourth in the wet/dry race at Toronto. In 2010 returned to the series to race for Bryan Herta Autosport. Wilson finished 11th in points despite missing one race due to funding issues and another due to a damaged racecar. He had a career-best finish of third in the season opener at St. Pete and ran the fastest race lap in Toronto. In 2011 he returned to Indy Lights full-time with Andretti Autosport. He captured one pole, two wins, and finished on the podium three more times to finish third in the championship. Despite Wilson's 2011 success he was out of racing until the 2012 Indy Lights season finale at Auto Club Speedway where he drove for Fan Force United and finished sixth.
IndyCar
Wilson made his IndyCar debut at the 2013 Grand Prix of Baltimore driving for Dale Coyne Racing, finishing sixteenth. His brother Justin drove the other full-time entry for Dale Coyne Racing, making the Wilson brothers the first pair of brothers to drive in IndyCar for the same team since Gary Bettenhausen and Tony Bettenhausen, Jr. drove for their family team in 1983. In June 2014 Fan Force United announced that they had signed Wilson for the team's full-time step up to the IndyCar Series in 2015. However, this entry ultimately did not materialize. On 26 April 2016 it was announced that Wilson will be driving for KV Racing Technology at the 100th Running of the Indianapolis 500. Wilson will be driving the No. 25 Driven2SaveLives Chevy. He chose No. 25 in honor of his late brother Justin, who drove the No. 25 car when he received his fatal injuries during an incident at the 2015 ABC Supply 500. Wilson nearly won the 2018 Indianapolis 500, but ran out of fuel with four laps to go, handing the victory to Will Power.
