Biela began racing in 1983 in karting before joining the Ford Youngster Team programme in 1987 alongside Manuel Reuter and Bernd Schneider. With Ford he competed in Formula Ford and the Deutsche Tourenwagen Meisterschaft, winning the DTM race at AVUS in 1987. He continued in DTM in 1988 and also ran a limited season in German Formula Three, scoring two victories.
In 1990 Biela joined Audi and won the DTM race at the Nürburgring that year. He then claimed the full DTM title in 1991 driving an Audi V8, cementing his reputation as the marque's lead touring car weapon. When Audi withdrew from DTM mid-season in 1992, Biela followed the manufacturer into the growing Super Touring category across Europe.
In 1993 he won the French Supertouring Championship driving an Audi 80, becoming the only non-French driver to win that title. He contested the German Super Tourenwagen Cup in 1994 and 1995, dominating the early portion of both seasons only to be denied the crown late in the year — losing to Johnny Cecotto and Joachim Winkelhock respectively. In September 1995 at the AVUS Berlin race, Biela's Audi struck the accident-stranded car of Keith O'Dor, who died later that day. He also won the 1995 Touring Car World Cup one-off race at Paul Ricard in the new Audi A4.
For 1996 Audi entered a two-car works team in the British Touring Car Championship, with Biela leading the effort alongside John Bintcliffe. The four-wheel-drive Audi A4 proved dominant throughout the season. Biela finished every single round and was classified in the top ten in all but two races, comfortably taking the title. He capped the year by winning the Guia Race of Macau in the Super Touring class. In 1997 BTCC organizers imposed a heavy ballast penalty on all four-wheel-drive cars. Despite the handicap, when the weight was halved at mid-season Biela responded strongly and finished second in the championship to Alain Menu.
After a difficult return to the German Super Tourenwagen Cup in 1998, Biela abandoned touring cars to join the Audi R8 sportscar programme under the Audi Sport Team Joest banner in 1999. The move proved transformative. Between 2000 and 2002 he won three consecutive 24 Hours of Le Mans alongside Emanuele Pirro and Tom Kristensen, a run of dominance that defined the era of Audi diesel and petrol prototype racing at La Sarthe.
He continued in sportscar competition, recording fourth in 2004 and third in 2005 at Le Mans. In December 2005 he participated in the first test runs of the new Audi R10 diesel prototype. Driving the R10 for Team Joest in 2006 alongside Pirro and Marco Werner, Biela took his fourth Le Mans victory. He repeated the success with the same car and team in 2007, bringing his total to five Le Mans wins — one of the highest totals in the race's history.
He also won the 12 Hours of Sebring four times (2000, 2003, 2004, 2007) and claimed two victories at Petit Le Mans (2001 and 2005), along with American Le Mans Series titles in the LMP900 class in 2003 and LMP1 in 2005.
Biela's career is distinguished by its singular loyalty to one manufacturer and by its breadth across disciplines. He is the only driver to have won the DTM, the BTCC, and five times at Le Mans. A 2005 poll by Motorsport Magazine readers voted him the 19th greatest touring car driver of all time, though his endurance record alone places him among the most successful sportscar racers of the 2000s.