Nannini was born in Siena and is the younger brother of musician Gianna Nannini. He began his motorsport career in national rally events, driving a Lancia Stratos, before switching to Formula Italia in 1981. From 1982 to 1984 he raced for Minardi in European Formula Two, attracting attention for his pace in uncompetitive machinery. His best Formula Two season placed him seventh overall in 1983. During the same period he was signed by Lancia for the World Sportscar Championship: he set fastest lap at the 1984 24 Hours of Le Mans (where he finished eighth with Bob Wollek) and won the 1984 1000 km of Kyalami alongside Riccardo Patrese. In 1987, in his spare time, he also paired with Giorgio Marin to win the Mille Miglia road race.
Nannini was Giancarlo Minardi's first choice to drive the team's new Formula One car in 1985, but was controversially denied a Super Licence by the FIA's governing body FISA, with former teammate Pierluigi Martini taking the drive instead. He was finally granted a licence for 1986 and joined Minardi, where he remained for two seasons. The Minardi-Motori Moderni package was uncompetitive, and Nannini was classified in only four of thirty starts. However, his raw speed caught the attention of the paddock, particularly his performances against the more experienced Andrea de Cesaris in 1986.
Benetton signed Nannini for 1988 to partner Thierry Boutsen. He scored his first point in his second race for the team and collected two third-place finishes on his way to tenth in the championship. With Boutsen departing for Williams, Nannini was promoted to team leader in 1989, partnered by Johnny Herbert. At Suzuka, following the collision between the two leading McLarens of Ayrton Senna and Alain Prost, Nannini inherited the lead and ultimately won the race after Senna — who had rejoined and passed Nannini — was disqualified for bypassing the chicane post-collision. That result remained the sole Formula One victory of Nannini's career. He closed the season with a strong second place in rain-soaked conditions at Adelaide, finishing sixth in the championship. For 1990, he was partnered by triple World Champion Nelson Piquet. Nannini matched Piquet in pace on several occasions, most notably at Hockenheim where he led for sixteen laps in the closing stages before fading grip surrendered second place to Senna. He had finished third in the Spanish Grand Prix when, the following week, the helicopter accident ended his Formula One career.
Despite only partially regaining use of his right hand, Nannini returned to racing in 1993. He competed in four seasons of the Deutsche Tourenwagen Meisterschaft (later the International Touring Car Championship) with Alfa Corse, finishing fourth in the 1994 DTM standings and third in the 1996 ITC standings. He then moved to the FIA GT Championship with Mercedes in 1997, winning a race at Suzuka and finishing sixth in the overall standings, before retiring from professional racing at the end of that year. He briefly emerged from retirement in 2007 to take part in the Grand Prix Masters championship for Formula One veterans.
Nannini's career is defined by the contrast between his evident speed — acknowledged by contemporaries including commentators Murray Walker and James Hunt — and the misfortunes that denied him greater success: two seasons in the uncompetitive Minardi-Motori Moderni, and a career-ending accident at the moment when Ferrari were reportedly considering him as a replacement for Nigel Mansell and McLaren's Ron Dennis was also monitoring him closely. He accrued one win, nine podiums, and two fastest laps in Formula One. After motorsport, Nannini built a chain of upmarket cafes bearing his name, with branches extending internationally.