Regazzoni was born in Mendrisio, Switzerland, on 5 September 1939, and grew up in Porza in the Italian-speaking Canton of Ticino. Switzerland had banned motor racing following the 1955 Le Mans disaster, so most of his early racing experiences were across the border in Italy. He began competing comparatively late, at the age of 24 in 1963, starting in his own Austin-Healey Sprite before moving up to a Mini Cooper in 1964.
In 1965, Regazzoni entered the European Formula Three championship with a Brabham, then moved to a De Tomaso in 1966, which brought him to the attention of Tecno. The Italian constructor offered him a Formula Two drive for 1968. At the 1968 Monaco Formula Three support race, he survived a terrifying accident when his car slid under an Armco barrier, the sharp metal edge passing across the top of the cockpit; he ducked just enough for it to miss his head.
During his time in Formula Two with Tecno, Regazzoni was implicated in the death of British driver Chris Lambert at the 1968 Dutch Formula Two race, accused of running Lambert's car off track while lapping him. He was fully exonerated at the subsequent inquest, though Lambert's father pursued a private action for five years before abandoning it. Regazzoni won the European Formula Two Championship with Tecno in 1970.
Ferrari gave Regazzoni his Formula One debut at the 1970 Dutch Grand Prix as part of their evaluation of younger talent alongside Ignazio Giunti. He immediately showed his pace, finishing fourth on debut, and went on to claim four podium finishes in his first season including a victory at the Italian Grand Prix at Monza. He finished third in the Drivers' Championship with 33 points, behind posthumous champion Jochen Rindt. After Giunti's death in a sports car race early in 1971, Regazzoni and Jacky Ickx became Ferrari's lead pairing. The 1971 and 1972 seasons brought only moderate results — three podiums in 1971, one in 1972 — as the Tyrrell-Stewart combination proved superior.
Regazzoni left Ferrari for the Marlboro-sponsored BRM team, joining a young Niki Lauda. The two became firm friends. At the South African Grand Prix, Regazzoni was pulled from burning wreckage after a large crash by Mike Hailwood, who later received the George Medal for his actions. The season was otherwise unsuccessful, yielding just two championship points.
Regazzoni recommended Lauda to Ferrari when Luca Cordero di Montezemolo overhauled the team for 1974, and both were signed. The year was Regazzoni's finest. Seven podium finishes, including victory at the German Grand Prix, kept him in championship contention until the final race in the United States. He needed only to finish ahead of Emerson Fittipaldi to take the title, but a defective shock absorber forced two pit stops and he finished eleventh. Fittipaldi won the championship by three points.
In 1975, Regazzoni won the Italian Grand Prix and the non-championship Swiss Grand Prix — the only Swiss driver to have won his home event. Ferrari won the Constructors' Championship and Lauda claimed the first of his three World titles. Regazzoni finished fifth in the standings.
In 1976, Regazzoni dominated the inaugural United States Grand Prix West at Long Beach from pole position, and added three further podiums. Following Lauda's near-fatal accident at the Nürburgring and the controversial end to the season in Japan, Ferrari replaced Regazzoni with Carlos Reutemann despite Lauda's objections. Regazzoni departed as Ferrari's longest-serving driver, having raced 73 times for the team — a record that stood for 12 years until Michele Alboreto broke it in 1988.
Regazzoni surprised observers by choosing Ensign over a Brabham offer from Bernie Ecclestone, preferring "to race with nice people." He also competed in the 1977 Indianapolis 500, qualifying for a McLaren-Offenhauser entry run by Theodore Racing but retiring with a fuel cell problem. A move to Shadow in 1978 produced only two points-scoring finishes.
Frank Williams signed Regazzoni alongside Alan Jones for 1979. The Williams FW07 was the most competitive car in the second half of the season, winning all but two of the final seven races. Regazzoni took the first of those victories, at Silverstone, giving Williams their first ever Formula One win. He was nonetheless replaced by Carlos Reutemann at the year's end.
Regazzoni rejoined Ensign for 1980. At the United States Grand Prix West in Long Beach, the brake pedal of his car failed at approximately 280 km/h on a long high-speed straight. His car struck a retired Brabham parked on the escape road and then the barrier. The crash left Regazzoni paralysed from the waist down and ended his Formula One career. He subsequently sued the race organisers over safety procedures; the organisers demonstrated the procedures were adequate and won the case.
Alongside single-seater racing, Regazzoni had an active sports car career with Ferrari. He partnered with Arturo Merzario at the 1970 24 Hours of Le Mans in a Ferrari 512S, retiring after 38 laps. In 1971 and 1972, regularly partnered with Jacky Ickx in Ferrari's 312P programme, he achieved second place at the BOAC 1000 km at Brands Hatch, won the Kyalami 9 Hours with Brian Redman, won the Imola 500 km first heat, and shared victory in the Monza 1000 km with Ickx.
After his accident, Regazzoni regained his racing licence and became one of the first disabled drivers to compete at a high level in motorsport, racing hand-controlled cars in the Dakar Rally and the 12 Hours of Sebring in the late 1980s and early 1990s. He became a television commentator for Swiss and Italian broadcasters from 1996. His autobiography È questione di cuore was published in the mid-1980s.
On 15 December 2006, Regazzoni was killed when the car he was driving struck the rear of a lorry on the A1 motorway near Parma, Italy. An autopsy excluded a heart attack as a cause. His funeral in Lugano on 23 December was attended by Niki Lauda, Arturo Merzario, Jackie Stewart, Emerson Fittipaldi, and Peter Sauber. He was 67 years old.
Regazzoni is portrayed by Pierfrancesco Favino in Ron Howard's 2013 film Rush, which depicts the 1976 championship rivalry between James Hunt and Niki Lauda.