After service in the Pacific with the United States Army Air Forces in World War II, Rosenman earned a bachelor's degree in music from the University of California, Berkeley.

[1] He composed scores for war films such as William Wellman's biographical Lafayette Escadrille (1958), Lewis Milestone's Pork Chop Hill (1959), Delbert Mann's The Outsider (1961), Don Siegel's Hell is for Heroes (1962), and the Combat!

He wrote incidental music for such television series as Law of the Plainsman, The Defenders, The Twilight Zone, Gibbsville, and Marcus Welby, M.D..[1] He went on to compose George Cukor's The Chapman Report, then Richard Fleischer's Fantastic Voyage (1966), where he rejected producer Saul David's instructions.

In 1995, Nonesuch Records issued an album of music from both East of Eden and Rebel Without A Cause, played by the London Sinfonietta conducted by John Adams.

He died March 4, 2008, of a heart attack at the Motion Picture & Television Country House and Hospital in Woodland Hills, Los Angeles, California.