Regazzoni began racing comparatively late, at the age of 24 in 1963, first in an Austin-Healey Sprite, then a Mini Cooper. Switzerland had banned motor racing following the 1955 Le Mans disaster, so most of his early competition took place across the border in Italy. He moved into Formula Three in 1965 with a Brabham, and by 1967 had attracted the attention of Italian constructor Tecno, who offered him a works Formula Three drive. In 1968 he nearly lost his head when his F3 car passed under an Armco barrier at Monaco, the roll hoop catching the rail just above his helmet. Tecno then moved him to Formula Two, where his hard-charging style proved ideal. In 1970, he took the European Formula Two Championship with the team.
Ferrari gave Regazzoni his debut at the 1970 Dutch Grand Prix, where he finished fourth. He retained the seat and delivered an extraordinary debut season: four podiums in the final six rounds, capped by victory at the Italian Grand Prix at Monza — the same race overshadowed by the death of championship leader Jochen Rindt. Regazzoni finished third in the Drivers' Championship that year with 33 points.
In 1974, Ferrari hired Regazzoni back alongside Niki Lauda — a partnership Regazzoni himself had recommended. He won the German Grand Prix at the Nürburgring and entered the final race of the season, in the United States, with a genuine title chance. A defective shock absorber relegated him to eleventh place, and he finished just three points behind champion Emerson Fittipaldi — the best result of his career.
In 1975, Ferrari won the Constructors' Championship and Lauda claimed the Drivers' title. Regazzoni scored one of the team's wins, taking the Italian Grand Prix at Monza, and also won the non-championship Swiss Grand Prix — the only Swiss driver ever to do so.
The 1976 season opened with a dominant win from pole at the inaugural Long Beach Grand Prix, but Lauda's serious accident at the Nürburgring destabilised Ferrari internally. Despite Lauda's protests, Regazzoni was replaced by Carlos Reutemann at the season's end. When he departed, Regazzoni held the record as the longest-serving Ferrari driver, having contested 73 races for the team.
Between his two Ferrari stints, Regazzoni spent a troubled 1973 season at BRM alongside the young Niki Lauda. The car was uncompetitive and his year was nearly ended at the South African Grand Prix when his car caught fire. He was pulled from the wreck by Mike Hailwood, who later received the George Medal for the act. Regazzoni scored just two points from the entire season.
After spells at Ensign and Shadow, Regazzoni joined Williams in 1979 alongside Alan Jones. The Williams FW07 was highly competitive in the latter part of the season, and Regazzoni gave the team its first-ever Grand Prix victory at the 1979 British Grand Prix at Silverstone — the first of what would become over 100 Williams victories. Despite this achievement, he was again replaced by Carlos Reutemann for 1980.
Regazzoni returned to Ensign for what proved his final campaign. At the 1980 United States Grand Prix West at Long Beach, his brake pedal failed at high speed. His car struck a stationary Brabham in the escape road and hit the barriers at approximately 280 km/h. The impact left him paralyzed from the waist down, ending his Formula One career. He was 40 years old.
Rather than retreating from motorsport, Regazzoni fought to regain his racing licence and became one of the first disabled drivers to compete at a high level. During the late 1980s and early 1990s he raced in the Paris–Dakar rally and at the Sebring 12 Hours using hand-controlled cars. His last competitive race came in 1990. In 1994 he returned to Long Beach as a competitor in the Toyota Pro/Celebrity Race. He later worked as a commentator for Swiss and Italian television. He wrote two books: his autobiography È questione di cuore ("It's a Matter of Heart") and E la corsa continua ("And the race goes on") about his Dakar experiences.
On 15 December 2006, Regazzoni was killed when the car he was driving struck the rear of a lorry on the Italian A1 motorway near Parma. He was 67. His funeral in Lugano was attended by Niki Lauda, Arturo Merzario, Jackie Stewart, Emerson Fittipaldi, and Peter Sauber, among others from the Formula One world. Jody Scheckter once said of him that if "he'd been a cowboy he'd have been the one in the black hat." He is remembered as a Ferrari icon and a symbol of competitive courage both on and off the track. He was portrayed by Pierfrancesco Favino in Ron Howard's 2013 film Rush.