Müller showed early promise by winning the German Formula Opel Lotus Challenge in 1989 and the European Formula Ford 1600 championship the same year. He claimed the prestigious Macau Grand Prix in 1993 and became German Formula Three Champion in 1994. His momentum carried into single-seaters' next rung: he won the International Formula 3000 Championship in 1996 for team RSM Helmut Marko, driving a Lola-Zytek — one of the clearest pathways to Formula One available at the time. He had also won the Spa 24 Hours in 1995–96.
From 1997 to 1998, Müller served as Formula One test driver for Arrows and Sauber-Petronas. He then joined the BMW-WilliamsF1 project from 1999 to 2001, testing engines and Michelin tyres. Despite this high-profile testing work across several seasons, a race seat never materialized. He became the first Formula 3000 champion since the series began to fail to make the step up to Formula One, a distinction that underlined how difficult that transition was even for title-holders.
While testing for Williams, Müller was simultaneously active in sportscar racing. He drove for Nissan and Porsche in the FIA GT Championship, and was part of the winning team at the 24 Hours of Daytona in a Porsche 911 GT1. In 1999 he was part of the BMW V12 LMR crew that led the 24 Hours of Le Mans for 18 hours before ultimately not winning.
In 2000 and 2001, Müller raced for BMW and Schnitzer Motorsport in the American Le Mans Series. He won the ALMS GT class title in 2001 driving the BMW M3 GTR V8 — a car that had been developed specifically for that campaign.
From 2002 onward, Müller became a mainstay of BMW's factory touring car programme, driving in the FIA European Touring Car Championship and its successor, the World Touring Car Championship (WTCC). He finished second in the WTCC in 2006, his best championship result in that series. He raced alongside teammates including Dirk Müller (unrelated) and later Augusto Farfus through 2009.
The 24 Hours Nürburgring was a particular hunting ground. In 2004, Müller and Dirk Müller, together with Hans-Joachim Stuck, won the race outright in the BMW M3 GTR V8. In 2010, Müller returned to overall victory at the Nürburgring 24 Hours in an M3 GT2, sharing with Augusto Farfus, Pedro Lamy, and Uwe Alzen. He defended in 2011 but finished second with the same core lineup.
After BMW concentrated factory resources on the DTM from 2012, Müller moved back to the American Le Mans Series, then ventured to the Super GT Championship in Japan from 2014, racing for BMW Team Studie for multiple seasons alongside Seiji Ara. Despite several near-wins, the partnership did not achieve a race victory but finished third in the overall standings in 2014.
Müller remained active in VLN endurance racing at the Nürburgring through 2017 and contributed to development work on the BMW M6 GT3, receiving the honour of driving the car on its first public roll-out at the BMW factory in Dingolfing in February 2015.
Müller is the son of former European karting champion Ewald Müller. He has a younger brother, Rainer, and an older sister, Marion, and resides in Monaco.