Biela, from Neuss, began his motorsport career in 1982 in karting and became German champion in this category just one year later. With notable successes in Formula Ford, he secured a place as a Ford works driver in the German Touring Car Championship in 1987. At the same time, he competed in the German Formula 3 Championship until 1989.
In the 1990 season, Biela joined the MS-Racing team of Jochen Mass and Günter Schons. He won in the 190 E 2.5-16 Evolution DTM already in the second DTM round on the occasion of the 24-hour race at the Nürburgring and achieved tenth position in the final drivers' standings.
in 1991, he switched to Audi and, in addition to winning a DTM title, went on to claim a total of five Le Mans victories for the Ingolstadt-based brand (2000 to 2002 as well as 2006 and 2007).