Wright was born in Pickwick Dam, Tennessee, and attended Davidson College and the University of Iowa Writers' Workshop. Wright has been widely published, winning the National Book Award in 1983 for Country Music: Selected Early Poems and the Pulitzer Prize for Poetry in 1998 for Black Zodiac. Other works include Chickamauga, Buffalo Yoga, Negative Blue, Appalachia, The World of the Ten Thousand Things: Poems 1980-1990, Zone Journals and Hard Freight. Wright's work also appears in an online journal of literature and the arts.
Wright has published two works of criticism, Halflife and Quarter Notes. His translation of Eugenio Montale's The Storm and Other Poems won him the PEN Translation Prize in 1979. In 1993, he received the Ruth Lilly Poetry Prize for his lifetime achievement. He is a Chancellor of The Academy of American Poets and Souder Family Professor of English at the University of Virginia in Charlottesville.