O'Donnell graduated from high school during World War II and then served in the U.S. Army Air Forces (1942–1945), where he flew 30 missions as a bombardier in a B-17 squadron before being shot down over Belgium. "He was imprisoned, escaped, and emerged with the Distinguished Flying Cross and Air Medal with Four Oak Leaf Clusters." Following the war, he studied at Harvard College (1946–1949) and met Robert F. Kennedy, where they were roommates as well as teammates on the Harvard football team; O'Donnell became team captain in 1948. The two remained close friends until Kennedy's assassination in 1968.