His family moved to the United States in 1920. He began on clarinet before switching to tenor sax. He is most associated with Stan Kenton who he first worked with in 1930. He reached his peak of notoriety with Kenton from 1945 to 1947. Perhaps his most notable work with the Kenton orchestra was his "Come Back to Sorrento". His son-in-law is comedian Shecky Greene. Musso died 9 January 1982 in Rancho Mirage, California.