Born in Rochester, New York, Famoudou performed in a church choir and various drum and bugle corps (marching ensembles) during his youth. He was exposed to jazz from an early age – his mother worked for a local social club, located door-to-door with a jazz venue that hosted musicians like Kenny Burrell and Jimmy McGriff, and often took her son to concerts, including Mahalia Jackson performances. Don Moye's uncles played saxophone, while his father was a drummer.
Moye studied percussion at Wayne State University in Detroit. A trumpeter Charles Moore, who happened to live in the same building, became Famoudou's mentor and introduced him to the Association for the Advancement of Creative Musicians (AACM). In 1968, Famoudou Don Moye travelled to Europe with his first band, Detroit Free Jazz. He eventually spent a few years abroad, working for RAI (Italian Radio and Television) briefly, and collaborating extensively with Moroccan musicians, as well as many notable jazz figures, such as Steve Lacy, Pharoah Sanders, Sonny Sharrock, Randy Weston, and Art Taylor.
In 1969, while rehearsing and performing at the American Center For Students And Artists in Paris, Moye met saxophonist Roscoe Mitchell, who was in Europe with his quartet The Art Ensemble of Chicago (also featuring Joseph Jarman (sax), Lester Bowie (trumpet) and Malachi Favors on bass). AEC already released three albums on BYG Records at the time, but four members were playing percussion parts themselves, and lacked a dedicated performer to complete a rhythm section. Roscoe Mitchell asked Don Moye to join the group.
After returning to the United States in the early 1970s, Famoudou Don Moye had played with Black Artists Group in St. Louis for a while, and finally settled in Chicago. Apart from an extensive work the The Art Ensemble Of Chicago, Moye also played in a duo with percussionist Steve McCall. In 1984, the musician joined The Leaders (3) jazz supergroup. Famoudou Don Moye played and recorded with different bands and ensembles of Don Pullen, Cecil McBee, Hamiet Bluiett, Julius A Hemphill, Chico Freeman and Lester Bowie's Brass Fantasy.
His recordings are universally recognized by critics at such prestigious publications as Rolling Stone, Melody Maker, The New York Times, Stereo Review, Audio Magazine, and Down Beat. Famoudou Don Moye received grants from the National Endowment For The Arts in 1974 and '81.