Müller started his career in the cabaret theatre Die Wühlmäuse in Berlin in 1959. He later worked on a large number of German-language television shows, and became a well-known voice-over actor, lending his voice to such actors as Danny DeVito, Nathan Lane, and Jason Alexander. Since 1991, he voices Krusty the Clown on the German version of The Simpsons, as well as several other supporting characters when the usual voice actor is unavailable.