Stewart was born in San Saba, Texas, in 1928. He studied at Juilliard, where he made his debut in 1954 as La Roche in the American premiere of Strauss's Capriccio. He also sang with New York City Opera and Lyric Opera of Chicago. He married the soprano Evelyn Lear in 1955, and frequently performed with her in both operas and recitals.

However, according to The New York Times, they both initially struggled in the music business, singing in churches and doing commercial work to make ends meet. By 1956 Stewart had decided to take a job with I.B.M., but both he and Lear were offered Fulbright scholarships to study in Germany.

Stewart made his debut with the Deutsche Oper Berlin in 1958 as Escamillo in Bizet's Carmen and remained on their roster until 1964. His Covent Garden debut was in 1960, again as Escamillo, and he sang frequently at the Royal Opera House until 1978. He made his Bayreuth debut in 1960, where he also appeared regularly until 1975. His Metropolitan Opera debut came in 1966, as Ford in Verdi's Falstaff, and he sang 192 performances until his last appearance in 1993.

The Times writes that Stewart was "a commanding singer, muscular and with a moustache and beard that seemed suited to the often imperious roles he sang. Yet his commanding quality came less from the size or mettle of his voice, which was surprisingly lyrical for a Wagner baritone, but from his imaginative approach to his roles. He gave his characters a measure of warmth and expressivity that often made them seem complex and surprising. The conductor Herbert von Karajan singled out Mr. Stewart as his favorite Wotan."

Apart from Wagner, Stewart also regularly sang Mozart, Verdi and Offenbach roles. He took the title role in the American premiere of Aribert Reimann's Lear in 1981 with the San Francisco Opera, where he also appeared frequently.

Stewart and Lear founded the Evelyn Lear and Thomas Stewart Emerging Singers Program, run with the Wagner Society of Washington, D.C., where they gave masterclasses.