Born in Chicago, Ware taught himself to play banjo and bass. In the 1940s, he worked with Stuff Smith, Sonny Stitt and Roy Eldridge. In the 1950s, Ware played with Eddie Vinson, Art Blakey, and Buddy DeFranco. He is best known for his work with the Thelonious Monk quartet in 1957-58. In 1969, Ware played with Clifford Jordan, Elvin Jones and Sonny Rollins. He later moved to Philadelphia, where he died from emphysema in 1979.