Born in Milan, Fabi studied mechanical engineering at Institute of Technology in Milan and raced motorcycles in his spare time. Between 1970 and 1974 he was a downhill ski racer.
He started racing cars in 1976 and rose rapidly through Formula Ford 1600, winning the 1977 Italian Championship, to race a private March in the European Formula 3 series in 1978. He scored three wins that year and finished fourth in the Championship.
He was signed by the March Formula 2 works team in 1979, finishing 10th in the European F2 series. The following year he moved up to third and F1 beckoned with the RAM March team in 1981, but the drive went to Derek Daly and Fabi went to America to race in CanAm for Paul Newman.
He won four races and was fortunate to emerge unscathed from a crash at Elkhart Lake.
In 1982 he was offered a Toleman Formula 1 drive alongside Derek Warwick. He also raced for the Lancia factory team in sportscars, winning the Nurburgring 1000 with Riccardo Patrese and Michele Alboreto.
F1 was a dissapointment and in 1983 he went to the USA to race for Forsythe Racing with a new March 83C. He won four races and took Rookie of the Year honors, just failing to take the CART title.
Set for another year with Forsythe, he received a call from Bernie Ecclestone to join the Brabham-BMW F1 team. He ended up running in both CART and F1 with his brother Corrado standing in for him at Brabham when his CART commitments overlapped. Midseason he handed his CART drive to Kevin Cogan so that he could concentrate on F1. Teo's best finish was a third at Detroit in the Brabham.
In the Autum his father died and he took six months off to run the family's talcum powder mine. He then joined the new Benetton team, scoring three pole positions but had only one third place in the way of results. He eft the team at the end of 1987.
In 1988 he went back to Indycars with the Quaker State March-Porsche. In 1989 he won at Mid-Ohio but the team pulled out in 1990 and he joined Tom Walkinshaw Racing's Jaguar sportscar team.
In 1991 he won the World Sportscar Championship with the Jaguar XJR-14.
He signed for Toyota Team TOM'S in 1992 and when the series was canceled at the end of the year Teo went back to CART with the Hall/VDS team who he stayed with until the end 1994 when decided to retire from racing.
Teo's son Stefano is now racing.