Moye studied percussion at Wayne State University in Detroit, where he worked with trumpeter Charles Moore's Detroit Free Jazz. Moore's band traveled to Europe in May of 1968. Once there, Moye traveled the continent and Northern Africa, working with such players as Steve Lacy, Sonny Sharrock, and Pharoah Sanders. In 1969, the Art Ensemble arrived in Paris. The band had been performing without a drummer in the two years since their inception. In Paris they decided to hire a full-time drummer and found Moye at the American Center for Students and Artists. Moye's extremely active, pattern-based polyrhythmic style lent the group a drive and cohesion that they had (to some degree) lacked. Along with Jarman and Favors, Moye took to wearing African face paint and clothing in performance with the Art Ensemble.

Moye has long been active in contexts apart from the Art Ensemble. Before moving to Chicago in 1971, Moye played with musicians associated with the Black Artists Group in St. Louis. In the '70s, he played with pianist Randy Weston and formed a percussion duo with fellow AACM member Steve McCall. Moye played and recorded in a variety of jazz settings, from modal to bop to free. In 1984, he became a member of the Leaders, a collection of avant-jazz all-stars Lester Bowie, Chico Freeman, Arthur Blythe, Don Cherry, and Kirk Lightsey. Moye recorded as a leader himself, notably on the Art Ensemble's own AECO label: in 1975, as a solo percussionist (Sun Percussion, Vol. 1); in 1993, as co-leader of the Joseph Jarman/Famoudou Don Moye Magic Triangle Band (Calypso's Smile); and in 1996, as co-leader, with Enoch Williamson of the Sun Percussion Summit (Afrikan Song).