Capelli began kart racing at age 15 and quickly progressed through Italian single-seaters. He won the Italian Formula Three championship in 1983 with nine victories, then claimed the European Formula Three championship in 1984 with the Coloni team. In 1985 he graduated to the European Formula 3000 championship with Genoa Racing, winning one race before making his Formula One debut that same year.
Capelli made his Formula One debut with Tyrrell at the 1985 European Grand Prix, finishing fourth in Australia later that season. Despite a promising start, he did not secure a full-time drive for 1986 and contested several races for the AGS team instead.
From 1987 Capelli raced full-time with the March team, guided by team boss Cesare Gariboldi, who had an almost father-son relationship with him. He scored March's first point with sixth place at the 1987 Monaco Grand Prix. His most impressive season came in 1988, when an Adrian Newey-designed March 881 powered by a Judd V8 made him a surprise frontrunner. He finished third at Spa-Francorchamps and second at the Portuguese Grand Prix, where he crossed the line behind Alain Prost. At the Japanese Grand Prix at Suzuka he briefly led the race, becoming the first naturally aspirated driver to lead a World Championship event since 1983, before an electrical failure ended his challenge.
The momentum faltered after Leyton House took a controlling interest in March. The 1989 season was difficult, with Capelli classified only twice in 16 starts. The death of Gariboldi in a car crash mid-season was a painful blow, yet team spirit held and Capelli exercised his option for 1990. That year, despite the CG901's sensitivity to bumps, Capelli delivered the team's best result: he led much of the French Grand Prix at Paul Ricard alongside teammate Mauricio Gugelmin before being overtaken by Prost's Ferrari with three laps remaining, finishing second. He was similarly promising at Silverstone and Hockenheim, but the French race remained the season's high point. In 1991 the Ilmor V10 engine programme added ambition but not results; when Leyton House's owner Akira Akagi was arrested over financial fraud, Capelli voluntarily stepped aside to allow pay driver Karl Wendlinger to finish the season.
In 1992 Capelli joined Scuderia Ferrari, becoming the first Italian with a regular Ferrari drive since Michele Alboreto in 1988. The new Ferrari F92A proved uncompetitive, and Capelli struggled to integrate with the team's bureaucratic structure. His motivation slipped, the team lost confidence, and he was released before the season ended — the only Ferrari driver up to that point who failed to reach the podium in a full season.
Jordan signed Capelli for 1993 alongside rookie Rubens Barrichello, but the spark never returned. After failing to qualify in Brazil he left the team by mutual consent and did not return to Formula One.
Capelli competed in touring cars from 1994 to the mid-2000s, including the German Super Tourenwagen Cup with BMS Scuderia Italia and later the Italian GT Championship and Trofeo Maserati, where he won races. From 1998 to 2017 he was a Formula One commentator and pundit for the Italian state broadcaster Rai 1.
Capelli's career is most often remembered for the 1988 and 1990 seasons, when an underfunded March/Leyton House team repeatedly threatened the top constructors. His brief lead at the 1988 Japanese Grand Prix symbolised how close the small team came to achieving greatness with limited resources. His move to Ferrari in 1992, notable for being the last Italian driver to hold a regular Ferrari seat for many years afterward, ended in disappointment that cut short what had been a genuinely promising Formula One career.