Born in Philadelphia, Woode launched his career in Boston, where he played at the Storyville and Hi Hat nightclubs with such visiting musicians as Charlie Parker, Miles Davis, and Billie Holiday. In 1955, he played for the Ellington band during a two-week engagement at Storyville and ended up joining the group permanently.
After five years with Ellington, Woode moved to Europe, where he performed with such fellow expatriates as pianist Bud Powell and saxophonist Don Byas. He played with the Kenny Clarke-Francy Boland Big Band from 1960 through 1973.
Woode moved back to the United States in 2001.