Müller started for the ASK Vorwärts Oberhof and the BSR "Rennsteig" Oberhof. During his career, he won 14 medals at the FIL World Luge Championships, including four gold (Men's singles: 2000, Mixed team: 1990, 1991, 1995), seven silvers (Men's singles: 1987, 1989, 1999; Mixed team: 1989, 1996, 1997, 2000), and three bronzes (Men's singles: 1985, 1990, 1996).