Green was raised in Milwaukee, Wisconsin, where he played the alto saxophone, mainly at a local club called “The Brass Rail”.
His first big break came when he was hired in New York City by Charles Mingus as a replacement for Jackie McLean in the 1960s. His brief stint with the eccentric bass player made a deep impression. Mingus’ sparing use of notation and his belief that there was no such thing as a wrong note had a lasting influence on Green’s own style.
The next year, Green moved to Chicago, Illinois, where he appeared with several prominent players including Sonny Stitt, Louie Bellson, Andrew Hill, Yusef Lateef, and Ira Sullivan. Originally strongly influenced by Charlie Parker, Green spent a period reassessing his style and studying, emerging with a highly distinctive sound that has deeply influenced a number of younger saxophonists, including Steve Coleman and Greg Osby.