Donald Harris served on the faculties and as an administrator at the New England Conservatory of Music (1967-77) and the Hartt School of Music, University of Hartford (1977-88), before becoming dean of the College of the Arts and professor of music at Ohio State in 1988. In 1997, after a thirty-year career as a senior-level administrator in higher education and the arts, he stepped down as dean and rejoined the OSU faculty in composition, becoming Professor Emeritus upon his retirement in 2010.

From 1955 until 1968, Harris lived and composed in Paris, France, where, among other things, he was music consultant to the United States Information Service, and produced the city's first postwar Festival of Contemporary American Music. Harris earned bachelor's and master's degrees in composition from The University of Michigan, where he was a student of Ross Lee Finney. He also studied with Lukas Foss and Boris Blacher at the Berkshire Music Center (Tanglewood), and with Nadia Boulanger, Max Deutsch, and André Jolivet in Paris.

He has received numerous commissions, including the Serge Koussevitzky Music Foundation, Elizabeth Sprague Coolidge Foundation, St. Paul Chamber Orchestra, Radio France, Cleveland Orchestra, Festival of Contemporary American Music at Tanglewood. He is co-editor of the W. W. Norton publication of the correspondence between Alban Berg and Arnold Schoenberg, for which he received an ASCAP Deems Taylor Award (1989). He has been the recipient of both a Guggenheim and a Fulbright Fellowship. In 1991, he was honored with an award in composition from the American Academy and Institute of Arts and Letters, which led to a retrospective recording of his work on the CRI label (1994). His music is published by the Editions Jobert in France, and in this country by GUNMAR Music, a division of G. Schirmer/AMP and Shawnee Press, and Theodore Presser, Inc. In addition to CRI, his compositions have been recorded on the Delos, Centaur, and NEC-Golden Crest labels. In 2010 his Second Symphony was premiered by the Columbus Symphony Orchestra. In June of th same year, the Ohio State University awarded him an honorary doctorate in recognition of his “distinguished career as an internationally recognized composer, arts administrator, teacher, and musicologist.”