Draeger studied at the Berlin-Reinickendorf Conservatory for Music and Art. Beginning 1953, he established himself as a familiar radio voice, and became the regular dubbing voice of such varied actors as Woody Allen, James Cagney, and Dudley Moore. He also dubbed Gene Wilder in Willy Wonka and the Chocolate Factory and Trans-American Express, Eric Idle as Sir Robin in Monty Python and the Holy Grail, George Harrison in The Beatles' films, Charles Grodin in Catch-22, Harry Dean Stanton in Repoman, Martin Landau in The Hallelujah Trail, and Roman Polanski in Chinatown.