He was born in Berlin, but his family left for the USA in 1938 and he became a US citizen in 1943. In 1967 he became conductor of the Houston Symphony Orchestra, and the following year added the London Symphony Orchestra to his portfolio, giving it a new, trendy image. In subsequent years, he was at various times conductor to the Pittsburgh Symphony Orchestra, the Royal Philharmonic Orchestra and the Los Angeles Philharmonic Orchestra. He composed film scores and musicals, a cello concerto and a guitar concerto, and is one of the world's best-known conductors. Previn received Kennedy Center Honors in 1998.
During his early career in Los Angeles, Previn arranged and composed movie scores, notably Three Little Words in 1950, Kiss Me Kate in 1953, It's Always Fair Weather in 1955, Silk Stockings in 1957, Bells Are Ringing in 1960, Irma La Douce in 1963, My Fair Lady in 1964 and Paint Your Wagon in 1969. In later years, he concentrated on classical music. His first opera, A Streetcar Named Desire premiered in San Francisco in 1998.
In the UK, he is particularly remembered for his performance on the Morecambe & Wise show, which involved his conducting a spoof performance of Grieg's Piano Concerto, with Morecambe as the soloist. Because of other commitments, the only time available for Previn to learn his part was during a transatlantic flight, but the talent he showed for comedy won high praise from his co-performers.
Previn's marriages, first to Dory Previn and then to Mia Farrow, have also kept him in the public eye. In 2002 he married the young violinist Anne-Sophie Mutter.