Alboreto was born in Milan. He began his motorsport career in 1976 in the Formula Monza series with a car he and friends had built themselves, known as the CMR. The car was uncompetitive and he moved to Formula Italia in 1978, where he started winning races. By 1980 he had taken the European Formula Three Championship and finished third in the Italian series. That title earned him a place in Formula Two with Minardi in 1981, where he scored the team's only F2 victory, at Misano.
Alongside his single-seater programme, Alboreto was chosen by Lancia for their World Championship for Makes campaign from 1980 onward, racing the Group 5 Lancia Beta Montecarlo and later the Lancia LC1 and LC2 prototypes. He won several endurance events during this period alongside partners including Riccardo Patrese, contributing to Lancia's competitive standing in the World Sportscar Championship.
Alboreto made his Formula One debut at the 1981 San Marino Grand Prix with Tyrrell, replacing Ricardo Zunino. His maiden championship season brought no points. In 1982 he took his first Grand Prix win at Las Vegas, the final running of the Caesars Palace Grand Prix, becoming the last winner of that event. A second win followed in 1983 at Detroit — the last victory for a naturally aspirated car before the end of the turbo era, and the 155th and last win for the Cosworth DFV engine — after championship leader Nelson Piquet suffered a rear tyre deflation late in the race. These results earned Alboreto a contract with Ferrari, where he became the first Italian driver to race for the Scuderia since Arturo Merzario in 1973, reportedly causing Enzo Ferrari to break his own rule against hiring Italian drivers.
At Ferrari in 1984, Alboreto won at Zolder, becoming the first Italian driver to win a Grand Prix for Ferrari since Ludovico Scarfiotti at the 1966 Italian Grand Prix. He finished the season fourth overall. The 1985 season was the high point of his career. He won the Canadian and German Grands Prix, led the points table until round 11 at Zandvoort, and challenged Alain Prost for the championship until Ferrari's late-season mechanical failures — he retired from the final five races through technical problems — allowed Prost to win the title by 20 points. Alboreto's 53 points gave him second place in the championship.
The following three seasons saw Ferrari decline in competitiveness. In 1986 the new F1/86 was slower and less reliable than its predecessor; Alboreto retired from nine races and scored only one podium. In 1987 Gerhard Berger joined the team and gradually became its de facto lead driver, winning in Japan and Australia while Alboreto managed only a handful of podiums. The 1988 season, Alboreto's last at Ferrari, brought only one win for the team — Berger at Monza — as the McLarens of Senna and Prost dominated the year. After 80 Grands Prix with the team, a record at the time, Alboreto was released.
A move to Tyrrell for 1989 turned sour quickly. At Monaco Alboreto was asked to race the older 017 model while teammate Jonathan Palmer used the new 018; he refused to accept the arrangement and boycotted a practice session. He subsequently left Tyrrell mid-season after the team asked him to end his personal Marlboro sponsorship to accommodate a new Camel deal. He joined Larrousse for the remainder of 1989, scoring no further points.
Seasons with Footwork (1990–1992), Scuderia Italia (1993), and Minardi (1994) followed. The Footwork period saw Alboreto score six championship points in 1992, his best return since leaving Ferrari. At Minardi in 1994 he picked up his only points finish of that season with a sixth place at Monaco. At the 1994 San Marino Grand Prix, a loose right rear wheel departed his car in the pitlane and bounced through the Benetton, Ferrari, and Lotus pit areas, injuring several mechanics. At the end of that season, with 194 starts and five wins, he retired from Formula One.
After leaving Formula One, Alboreto moved into the Deutsche Tourenwagen Meisterschaft with Alfa Romeo and later the IndyCar Racing League in 1996. He entered the 1996 Indianapolis 500 with Scandia/Simon Racing, finishing the race. His most celebrated late-career results came in endurance racing: the 1997 24 Hours of Le Mans with Joest Racing, sharing a Porsche WSC-95 with Stefan Johansson and Tom Kristensen, who would later break the Le Mans victory record. The trio completed 361 laps, one more than the second-placed BMW McLaren F1 GTR. Alboreto also won the 2001 12 Hours of Sebring with Audi, his final major victory.
On 25 April 2001, a month after Sebring, Alboreto was testing an Audi R8 at the EuroSpeedway Lausitz in preparation for that year's Le Mans. At approximately 300 km/h, a rear tyre failed due to a gradual loss of air pressure caused by a loose screw that had worked into the tyre. The car was launched over an Armco barrier and landed inverted; Alboreto's head struck the ground and he died instantly. Audi subsequently expedited the development of a sensor-based tyre pressure monitoring system for their race cars.
The final corner at Monza, the Curva Parabolica, was officially renamed the Curva Alboreto in August 2021 to mark the 20th anniversary of his death. Giancarlo Fisichella, who took a podium at Monza in 2005 — the first Italian driver to finish on the Monza podium since Alboreto — dedicated the result to his memory. Alboreto's helmet design used blue and yellow in tribute to Swedish driver Ronnie Peterson, a friend since 1972 who died from injuries sustained at the 1978 Italian Grand Prix; the two had met early in their careers and Alboreto maintained the colour tribute throughout his racing life.