Hunter was born in New York City, the son of Gertrude (nee Gelien) and Charles Kelm. His mother, from Hamburg, was a German Roman Catholic immigrant, and his father was Jewish. Hunter's father was reportedly abusive, and within a few years of his birth, his parents divorced. Tab grew up in California with his mother, older brother Walter, and maternal grandparents, John Henry and Ida (nee Sonnenfleth)

Hunter had a 1957 hit record with the song "Young Love," which was No. 1 on the Billboard Hot 100 chart for six weeks (seven weeks on the UK Chart) and became one of the larger hits of the Rock 'n' Roll era. It sold over one million copies, and was awarded a gold disc by the RIAA.  He had the hit, "Ninety-Nine Ways," which peaked at No. 11 in the US and No. 5 in the UK. His success prompted Jack L. Warner to enforce the actor's contract with the Warner Bros. studio by banning Dot Records, the label for which Hunter had recorded the single (and which was owned by rival Paramount Pictures), from releasing a follow-up album he had recorded for them. He established Warner Bros. Records specifically for Hunter.  Hunter's acting career was also at its zenith. William Wellman used him again in a war film, Lafayette Escadrille (1958). Columbia Pictures borrowed him for a Western, Gunman's Walk (1958), a film that Hunter considers his favorite role.  Hunter starred in the 1958 musical film Damn Yankees, in which he played Joe Hardy of Washington, D.C.'s American League baseball club. The film had originally been a Broadway show, but Hunter was the only one in the film version who had not appeared in the original cast. The show was based on the 1954 best-selling book The Year the Yankees Lost the Pennant by Douglass Wallop. Hunter later said the filming was hellish because director George Abbott was only interested in recreating the stage version word for word.  He also starred in They Came to Cordura (1959), with Gary Cooper and Rita Hayworth. Sidney Lumet starred him opposite Sophia Loren in That Kind of Woman (1959).

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Hunter starred in the 1958 musical film Damn Yankees,