Born in Roskilde, Magnussen won the 1992 Formula Ford Festival at Brands Hatch, then delivered one of the most dominant performances in British Formula 3 history by winning fourteen of eighteen events in the 1994 British Formula 3 Championship with Paul Stewart Racing — breaking Ayrton Senna's long-standing Formula 3 records in the process. Team founder Jackie Stewart described him as "the most talented young driver to emerge since Ayrton Senna."
Magnussen made his Formula One debut at the 1995 Pacific Grand Prix at Aida, substituting for an unwell Mika Häkkinen — becoming the first Danish driver to race in Formula One since Tom Belsø in 1974. For 1997 and 1998, Magnussen was a full-time driver at Stewart Grand Prix, the team co-owned by his former F3 boss Paul Stewart and his father Jackie Stewart. His Formula One career yielded a single championship point, scored at the 1998 Canadian Grand Prix. He started 24 Grands Prix in total, one fewer than he entered: his car was damaged in a start-line accident at the 1997 Brazilian Grand Prix before the restart.
Magnussen participated in the CART series in 1996 and again in 1999, making seven races in the latter season. He also drove in the International Touring Car Championship in 1996. His open-wheel career in North America gave way to a sustained focus on sports car racing.
From 1999 onwards, Magnussen was a fixture at the 24 Hours of Le Mans, competing every year. He joined Corvette Racing and won the GTS class at Le Mans in 2004, followed by GT1 class victories in 2005 and 2006 alongside Oliver Gavin and Olivier Beretta, and again in 2009 with Johnny O'Connell and Antonio García. He won the 12 Hours of Sebring in the GT1 class in 2006, 2008, and 2009.
Magnussen and García won the 2015 24 Hours of Daytona in the GTLM class. The two drivers competed as regular teammates in the IMSA WeatherTech SportsCar Championship in Chevrolet Corvette C7.R machinery, and Magnussen claimed the IMSA Sportscar Championship in 2017 and 2018. He also won the GT1 drivers' championship in 2008 and the GT drivers' championship in 2013, both with Corvette Racing. Magnussen remained a factory GM driver until the end of the 2020 season.
In Denmark, Magnussen competed in the Danish Touring Car Championship over many years, winning the DTC title in 2003 and 2008. He made a NASCAR Sprint Cup Series debut at Infineon Raceway in 2010, driving the No. 09 Chevrolet for Phoenix Racing and finishing twelfth from a thirty-second starting position.
In 2010, Magnussen co-drove the No. 57 Stevenson Motorsports Chevrolet Camaro at the Rolex 24 at Daytona in the GRAND-AM Rolex Sports Car Series, alongside Robin Liddell and Andrew Davis. He later competed in a full season of GRAND-AM with Stevenson.
In July 2023, Magnussen won the Aurum 1006 km endurance race in Lithuania, driving a Mercedes-Benz AMG GT3 Evo.
Magnussen's eldest son Kevin Magnussen has competed in Formula One with McLaren, Renault, and Haas, and in endurance racing with BMW. His nephew Dennis Lind and youngest son Luca are also racing drivers. Kevin has credited his father as his first hero in motorsport.