He was taught how to play piano and violin before focusing on saxophone; he was eventually invited to play with Duke Ellington's Orchestra in 1935.
He toured with the Jazz at the Philharmonic Orchestra in the 1950s.
He was born and grew up in Kansas City, Missouri.
Webster recorded a classical album called The Tatum Group Masterpieces, Vol. 8 with Art Tatum, Red Callender, and Bill Douglass.