He is best known for founding the Institute for Studies in American Music at Brooklyn College of the City University of New York in 1971.
After studying under Nadia Boulanger in Paris, he earned his Ph.D. at the University of Michigan in 1954.
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.