O'Donnell was born in Worcester, Massachusetts, and raised in Boston. Both of his parents were Catholics of Irish descent. He was the son of Alice M. (Guerin) and Cleo Albert O'Donnell, who was the football coach at the College of the Holy Cross Crusaders for two decades, and later athletics director for all sports activities. O'Donnell's older brother, also named Cleo, was a football star at Harvard during the 1940s.
