He was a featured vocalist on the George Burns and Gracie Allen radio program. On the show Allen playfully flirted with Tony, often threatening to fire him. She'd say things like "Oh Tony you look so tired, why don't you rest your lips on mine." In films, he was first cast in a number of bit parts, including a role as a sailor in the movie Follow the Fleet (1936), starring Fred Astaire and Ginger Rogers. He eventually signed with 20th Century-Fox and then Metro-Goldwyn-Mayer in which he starred in a number of musicals. Between 1938 and 1942, he made a number of hit records for Decca. Martin was featured in the 1941 Marx Brothers film The Big Store, in which he played a singer and performed Tenement Symphony, which was written by Hal Borne who became his long-time musical director. He appeared in film musicals in the 1940s and 1950s. His rendition of "Lover Come Back To Me" with Joan Weldon in Deep in My Heart - based on the music of Sigmund Romberg and starring José Ferrer - was one of the highlights of that film.
He also starred as Gaylord Ravenal in the Showboat segment from the 1946 film Till the Clouds Roll By.
NYTImes Obit Martin died on the evening of July 27, 2012, of "natural causes" at the age of 97.