Morris spent his formative years in New Haven, Connecticut, where he taught himself the guitar and immersed himself in a variety of progressive musical styles. He spent numerous weekends attending free symphonic productions at nearby Yale University, which included performances of artists as diverse as Karlheinz Stockhausen, Charles Ives, and Duke Ellington. Attention to local AACM (Association for the Advancement of Creative Musicians) members Leo Smith and George Lewis, and a world music radio show presented by percussionist Gerry Hemingway, also helped Morris develop his wide musical palette. In 1975, he moved to Boston, where his unique approach was not initially accepted in the then-prevalent modal jazz scene. Despite this temporary setback, and some time spent playing guitar in Europe, he developed a pivotal collaborative relationship with multi-instrumentalist Lowell Davidson, whose unique sound explorations inspired him to further develop his own original approach to music-making.

In 1981, Morris began his own label, Riti Records (named after an African single-stringed folk instrument), to document his prolific musical output. During the '90s he arguably became the most widely heralded free jazz guitarist in jazz, while recording with many avant-garde luminaries. Morris became the first guitarist to lead a recording session for the prestigious Black Saint/Soul Note Records with 1994's Symbolic Gesture, and he has continued to record extensively for many outstanding labels such as ECM, Hat Hut, Leo, Incus, Okka Disk, Homestead, About Time, Knitting Factory Works, No More Records, AUM Fidelity, and Omnitone. Also, Morris has given lectures and workshops for Harvard University, the New England Conservatory, the Berklee College of Music, and European universities.