Harrison began playing clarinet at age seven, and switched to tenor saxophone in high school. He studied under Barry Harris before moving to New York City in 1960. There he played with Jack McDuff, Elvin Jones, Sonny Stitt, Grant Green, Hank Crawford, and Sun Ra in the 1960s. In 1970 he moved back to Detroit and has remained a mainstay of the music scene there for over forty years.
In addition to albums as a leader, Harrison has worked as a session musician, and has a long list of famous artists with whom he has recorded. Early collaborations included recordings and concerts with premier jazz, R&B, soul, and Motown musicians, including Aretha Franklin, Sun Ra, and Marvin Gaye.
Harrison co-founded the Tribe record label and collective with Phil Ranelin in the 1970s. In the 1980s, he initiated the construction of a non profit “jazz performance and education organization”; Rebirth Inc. Two related record labels; Rebirth Records, and Wen-Ha Records are the product of Rebirth, Inc. He has worked as an educator, and played with Leon Thomas, Marcus Belgrave, Dennis Rowland, Kirk Lightsey, Roy Brooks, Charles Tolliver, and James Carter, among many other famous jazz musicians. Also, Harrison has collaborated with performers outside the jazz realm, such as techno artist Carl Craig, rapper Proof, R&B artist Amp Fiddler, and world music performer Sean Blackman.