Born in Roskilde, Denmark, Magnussen began his motorsport career in lower formula racing.
Magnussen won the 1992 Formula Ford Festival at Brands Hatch. He then dominated the 1994 British Formula 3 championship with Paul Stewart Racing, winning fourteen of eighteen events and breaking Ayrton Senna’s previous F3 record. He secured his first British F3 win that April at Donington Park, also taking pole position for the race. Further wins followed at Brands Hatch, Silverstone (twice), and Thruxton, establishing his dominance early in the season. He continued his success, winning again at Donington Park and both season-ending rounds at Silverstone.
Magnussen made his Formula One debut at the 1995 Pacific Grand Prix in Aida, substituting for Mika Häkkinen. He became the first Danish driver to race in Formula One since Tom Belsø in 1974. In 1997–1998, he raced for Stewart Grand Prix, a team co-owned by his former F3 boss, Paul Stewart. Jackie Stewart described him as “the most talented young driver to emerge since Ayrton Senna”, though his performance was ultimately underwhelming. He scored his only championship point at the 1998 Canadian Grand Prix, before being replaced by Jos Verstappen for the remainder of the season. He started 24 Grands Prix, one less than he entered, due to a race-ending accident at the start of the 1997 Brazilian Grand Prix.
Following his time in Formula One, Magnussen competed in various series. In 1999, he participated in seven CART races. He raced in the American Le Mans Series with Panoz in 1999 and 2000, and in 2001, drove a Peugeot in the Danish Touring Car series (DTC), also competing in eight ALMS races. He continued racing for Peugeot in DTC in 2002, alongside ten ALMS races.
Magnussen’s success with Corvette Racing began in 1999, with consistent participation in the 24 Hours of Le Mans. He achieved class victories in the GTS class in 2004 and GT1 class in 2005, 2006, and 2009, each time partnering with Oliver Gavin and Olivier Beretta (2005 & 2006) and Johnny O'Connell and Antonio García (2009) in a Chevrolet Corvette. He also secured GT1 class wins at the 12 Hours of Sebring in 2006, 2008, and 2009.
In 2010, Magnussen made his NASCAR Sprint Cup Series debut, driving the No. 09 HendrickCars.com Chevrolet for Phoenix Racing at Infineon Raceway, finishing twelfth after starting 32nd.
Magnussen continued to be an active driver, competing in the Danish Touring Car Championship (DTC) until 2010 and in a Chevrolet Corvette C7.R in the WeatherTech SportsCar Championship with Antonio Garcia until 2019, as well as the 24 Hours of Le Mans. He won the DTC in 2003 and 2008. In 2015, he won the 24 Hours of Daytona in the GTLM class. On 22 July 2023, he won the Aurum 1006 km endurance race in Lithuania, driving a Mercedes-Benz AMG GT3 Evo. On 16 September 2024, it was announced that Magnussen would participate in the Walter Hayes Trophy at Silverstone in November, driving a Van Diemen RF78 in Duckhams colours.
Magnussen’s oldest son, Kevin, is also a racing driver, currently competing in the FIA World Endurance Championship and IMSA WeatherTech SportsCar Championship with BMW, having previously raced in Formula One with Haas, McLaren and Renault. Kevin has stated that his father was his first hero. Magnussen’s nephew, Dennis Lind, and his youngest son, Luca, are also racing drivers.