Martin was active principally as an arranger for some of the most popular swing jazz bands of the 1930s and 1940s. He worked with Count Basie, Charlie Barnet (1939–40), Benny Goodman (1941), and Glenn Miller (1941–42); doubling as a reedist with the last three. In the Goodman orchestra he played alto sax alongside Gus Bivona and recorded with the legendary trumpeter Cootie Williams in the early 1940s as well.
Later in the 1940s he worked with Les Brown (memorably the big-band chart for I've Got My Love to Keep Me Warm), then moved to Los Angeles in the 1950s, where he did extensive work as a staff and freelance orchestrator, studio conductor (e.g. Astaire's Royal Wedding, 1951) and popular song arranger (often for Tony Martin, The Pied Pipers, the Andrews and De Castro sister groups, or Barbara Ruick).
Martin also recorded three albums as a leader and produced material for West Coast jazz and swing concept albums (e.g. 1959's Scheherajazz with Gus Bivona) for Somerset Records. In 1963 he joined Nelson Riddle on a dream team of arrangers working on the Sinatra-Burke compilation albums for the ambitious Reprise Musical Repertory Theatre project, featuring the singing members of the Rat Pack, plus Bing Crosby, Rosemary Clooney and Jo Stafford.
In Hollywood, Martin was one of the stellar team of orchestrators contributing to Singin' in the Rain (1952) and Guys and Dolls (1955). He frequently shared arrangement credits with Conrad Salinger, such as on Summer Stock (1950), Kiss Me Kate (1953) and Funny Face (1957). But perhaps his greatest work was as the sole credited orchestrator for Judy Garland's comeback vehicle A Star Is Born (1954), which contains many memorable arrangements by him of Harold Arlen and Ira Gershwin ballads, principally "The Man that Got Away" and "It's a New World".