He learned to play piano and cello as a child before switching to drums.
In the 1930s, West played in Chicago with Tiny Parham, Erskine Tate, and Roy Eldridge (1937–38).
Early in the 1940s he played with Hot Lips Page, and played on the early bebop scene at Minton's Playhouse in New York City with Dizzy Gillespie, Charlie Parker, Tiny Grimes, and Don Byas.
He played with Oscar Pettiford in 1944 and stood in for Jo Jones occasionally in Count Basie's orchestra.
West appears on recordings from Slam Stewart, Leo Watson, Wardell Gray, Billie Holiday, Erroll Garner, Big Joe Turner, and Jay McShann.