Born in Boston, Massachusetts, Murphy worked for Literary Digest in the 1930s before leaving in 1937 to work in the short film department at MGM. Murphy's first screenwriting credit was for providing the story for Back in the Saddle, a 1941 Gene Autrywestern.
While in the Army Air Forces during World War II, Murphy reached the rank of captain seeing action in the Pacific theater countries of New Guinea and the Philippines. Murphy returned to the States and started working for 20th Century Fox. In 1947 he wrote the award-winning film Boomerang. He received the first of two Oscar nominations for this screenplay, with his second in 1953 for the World War II film The Desert Rats. He also directed a few films before moving into television in the 1960s when he wrote and created television series. Murphy's last screenplay was for The Kidnapping of the President in 1980.