Veatch was born in Evansville, Indiana. He obtained his Ph.D. from Harvard University in 1937 and spent his career at Indiana University (1937–1965), Northwestern University (1965–1973), and Georgetown University (1973–1983) where he was Philosophy Department Chair from 1973 to 1976. He also had visiting professorships at Colby College, Haverford College and St. Thomas University. Veatch was active in the Episcopal Church and served as president of the American Catholic Philosophical Association. He served as president of the Metaphysical Society of America in 1961. In 1970–71 he served as president of the Western Division of the American Philosophical Association. He was a member of the Guild of Scholars of The Episcopal Church. Henry Veatch died in Bloomington, Indiana. Indiana University maintains the archive of his collected papers (1941–1997).