His son is saxophonist Joshua Redman.
Redman was born in Fort Worth, Texas. He attended I.M. Terrell High School, and played in the school band with Ornette Coleman, Prince Lasha and Charles Moffett. After high school, Redman briefly enrolled in the electrical engineering program at the Tuskegee Institute in Alabama, but became disillusioned with the program and returned home to Texas. In 1953, Redman earned a bachelor’s degree in Industrial Arts from Prairie View Agricultural and Mechanical University.