With Tom Stoppard, Norman won the Oscar for Best Original Screenplay in the 71st Academy Awards of 1998, for his script of Shakespeare in Love; he also shared in the Best Picture Oscar for the film as co-producer. Norman and Stoppard also won the Silver Bear for an outstanding single achievement at the 49th Berlin International Film Festival.
He wrote an episode of the Mission: Impossible TV series.
Norman is the author of Bike Riding in Los Angeles. A Novel (New York: Dutton 1972) and What Happens Next?: A History of Hollywood Screenwriting (New York: Harmony Books 2007; UK: Aurum Press 2008).