Murphy's parents divorced when he was three and his father was murdered not long afterwards. He and his brother were then placed in foster care until their mother remarried, when he was nine, and they went to live with her on Long Island.
He began stage performing when he was 15 and soon became popular on the television show Saturday Night Live (1981-84). His first film was 48 Hours (1982), and he has also starred in Trading Places, Beverly Hills Cop, Beverly Hills Cop II and III, Coming to America, Boomerang, The Distinguished Gentleman, The Nutty Professor, The Golden Child, Vampire in Brooklyn, and Metro.