Müller is the son of European karting champion Ewald Müller and grew up in the Netherlands before building his career in Germany. He won the German Formula Opel Lotus Challenge in 1989 and the European Formula Ford 1600 title the same year, establishing himself quickly in junior single-seaters. He went on to claim the German Formula Three championship in 1994 and the prestigious Macau Grand Prix in 1993. In 1996 he won the International Formula 3000 championship with team RSM Helmut Marko. Despite this résumé, Müller never made a Formula One race start, serving as a test driver for Arrows and Sauber-Petronas from 1997 to 1998, and later for BMW-Williams on engine and tyre development from 1999 to 2001 — making him the first F3000 champion since the series began not to convert his title into an F1 race seat.
Alongside his single-seater work, Müller built a strong sportscar record. He was part of the crew that won the 24 Hours of Daytona in a Porsche 911 GT1 and led the 1999 24 Hours of Le Mans for 18 hours in a BMW V12 LMR before falling short of victory. In the American Le Mans Series he won the GT class title in 2001 driving a BMW M3 GTR V8 for Schnitzer Motorsport. He returned to ALMS in 2012, sharing a BMW with Bill Auberlen and claiming a win and three podiums.
From 2002 to 2009 Müller drove BMW 3 Series touring cars for BMW Team Deutschland — the Schnitzer-operated factory squad — in the European Touring Car Championship and its successor the World Touring Car Championship. He finished second in the WTCC in 2006, his best championship result in the series. Team-mate Dirk Müller (unrelated) left after 2006; Augusto Farfus then partnered Jörg Müller for the 2007–2009 seasons, with championship finishes of seventh, seventh, and sixth. BMW cut its WTCC programme to two cars for 2010 and Müller departed the series.
The 24 Hours Nürburgring became a highlight of Müller's career. He shared a WTCC-spec BMW M3 GTR V8 victory in 2004 with Dirk Müller and Hans-Joachim Stuck. After leaving the WTCC, Müller won the 2010 edition outright in a BMW M3 GT2 alongside Augusto Farfus, Pedro Lamy, and Uwe Alzen. The defending champion crew returned for 2011 but placed second.
From 2013 Müller competed in the ADAC GT Masters with Schubert Motorsport and made repeat appearances at the Spa 24 Hours. In 2014 he joined BMW Sports Trophy Team Studie for a full Super GT season in Japan, finishing third in the championship alongside Seiji Ara with a podium assist from Farfus at Suzuka. He participated in development driving for the BMW M6 GT3, conducting the car's first roll-out at the BMW factory in Dingolfing in February 2015. He continued Super GT appearances into 2016 and in May that year co-drove the BMW M6 GT3 to its first overall VLN victory alongside Marco Wittmann and Jesse Krohn. Müller served throughout as a trusted BMW works driver and contributed to the development and mentoring of BMW Motorsport juniors well into the 2017 season.
Müller's career illustrates the pathway of a highly credentialed single-seater driver who found his greatest sustained success in GT and touring-car machinery. His WTCC vice-championship in 2006 represents one of BMW's stronger individual results in the series, and his multiple Nürburgring 24 Hours victories underline his endurance-racing pedigree. He holds the distinction of being a Formula 3000 champion who never reached a Formula One race start despite years of factory test work, a footnote that made him something of an anomaly in an era when the F3000 title was regarded as a near-certain F1 stepping stone.