The New York Times said Martin, who died Friday, formed his first band at California's Oakland Technical High School and was still performing in nightclubs around the United States until recently.
He frequently collaborated with his wife, dancer and actress Cyd Charisse, who predeceased him in 2008 after 60 years of marriage. She was 86.
They chronicled their lives together in the 1976 memoir "The Two of Us."
Born Alvin Morris in San Francisco, the singer changed his name when he got to Hollywood, where he worked in nightclubs, radio and television. He was known for his songs "Begin the Beguine," "There's No Tomorrow" and "I Get Ideas," as well as the films "Sing and Be Happy," "Follow the Fleet," "Sing, Baby, Sing," "Ziegfeld Girl," "Here Come the Girls" and "Hit the Deck," the Times said.
Martin and Charisse's son, Tony Martin Jr., died last year.