Hitchcock received a B.A. degree from Dartmouth College in 1944 and an M.A. from the University of Michigan in 1948. After study under Nadia Boulanger in Paris, he took his Ph.D. at the University of Michigan in 1954. He taught there from 1950-1961 and then at Hunter College from 1961 to 1971. He taught in the CUNY system until 1993, when he retired. He served as president of the Music Library Association, 1966-1967, the Charles Ives Society, 1973-1993, and the American Musicological Society, 1990-1992.
Hitchcock did much work on music of the early Baroque in France and Italy, especially on Marc-Antoine Charpentier. He also made important contributions to the understanding of musical traditions in America, both popular and cultivated, and his text in this field is a standard reference work. In addition to Charles Ives, he focused particular attention on contemporary American composers including Virgil Thomson, John Cage, and Henry Cowell. He was the co-editor of the New Grove Dictionary of American Music and a consultant for American music for The New Grove Dictionary of Music and Musicians.