Raised in Cincinnati, Ohio, Matthews earned a bachelor's degree from Yale University, and a master's from the University of North Carolina at Chapel Hill.
In addition to serving as a Writer-in-Residence at Boston's Emerson College, Matthews held various academic positions at institutions including Cornell University, the University of Washington (Seattle), the University of Colorado at Boulder, and the University of Iowa.He served as president of Associated Writing Programs and of the Poetry Society of America.At the time of his death he was a professor of English and director of the creative writing program at City College of New York A reading series has been named for him at City College of New York. His son is Sebastian Matthews.
Matthews published 11 books of poetry, including Time & Money which won the National Book Critics Circle Award in 1996 and was a Lenore Marshall Poetry Prize finalist. Two posthumous collections have been released: Search Party: Collected Poems and After All: Last Poems. Frequent subjects in his writing are the early years of professional basketball and historical Jazz figures.
Matthews believed that poetry should have subject matter, so as to provide the substance needed for the art to fulfill its function.