Tucker began at age 14, to appear as a jazz musician and studied at the Juilliard School and the New York Institute of Music and Arts. First, he played with the Barons of Rhythm. After his three years of military service in 1946, he was first a member of the band by Tony Scott and Mildred Bailey. He was known as a pianist and musical director of the trio of Billie Holiday, where he was employed from 1946 to 1949. He accompanied them on their 1947 Jazz at the Philharmonic show in New York's Carnegie Hall and recorded with her trio ( John Levy, and Denzil Best), for example, in 1948, " I Loves You Porgy ". In 1949, he joined Billy Eckstine, in which he served until his death as musical director. Among other things, he worked in 1960 at the Roulette album No Cover, No Minimum with. During this time he also played with Lucky Thompson, Stuff Smith, Sonny Criss, Babs Gonzales and Wardell Gray / Dexter Gordon All-Stars. He then worked with Johnny Hartman, with Lena Horne and with Antonio Carlos Jobim. The mid-1990s he toured with Tony Bennett. He also took on with Kenny Clarke, Paul Quinichette, Les Thompson and 1993 with Joe Wilder. With his own trio in 1960, he played the album Too Tough one, his only album as a leader.