Harris was born in Chandler, Oklahoma, of mixed Scots, Irish and Welsh ancestry, in circumstances he sometimes liked to contrast with those of the more privileged East-coast composers: to poor parents, in a log cabin in Oklahoma, on Abraham Lincoln's birthday, one of five children (three of whom died early). The boy grew up a farmer in this rural, isolated environment.
He studied piano with his mother, and later clarinet.
Though he studied at the University of California, Berkeley, he was still virtually self-taught when he began writing music of his own, but in the early 1920s he had lessons from Arthur Bliss (then in Santa Barbara) and the senior American composer and researcher of American Indian (then called "Red Indian") music, Arthur Farwell.
Harris sold his farmland and supported himself as a truck-driver and delivery man for a dairy firm. Gradually he made contacts in the East with other young composers, and partly through Aaron Copland's recommendation he was able to spend 1926-29 in Paris, as one of the many young Americans who received their final musical grooming in the masterclasses of Nadia Boulanger. Harris had no time for Boulanger's neoclassical, Stravinsky-derived aesthetic, but under her tutelage he began his lifelong study of Renaissance music, and wrote his first significant work: the Concerto for Piano, Clarinet and String Quartet.
During the 1930s Harris taught at Mills College, Westminster Choir College (1934–1938) and the Juilliard School of Music. He spent most of the rest of his professional career restlessly moving through teaching posts and residences at American colleges and universities. His final posts were in California, first at UCLA and then at California State University, Los Angeles. Among his pupils were William Schuman, H. Owen Reed, John Donald Robb, Robert Turner, Lorne Betts, George Lynn, John Verrall, and Peter Schickele (best known as the creator of P.D.Q. Bach). He received many of America's most prestigious cultural awards, and at the end of his life was proclaimed Honorary Composer Laureate of the State of California.