Kelleher was born in Camden, New Jersey, on March 12, 1931, and raised in Audubon, New Jersey, where he graduated from Haddon Heights High School. He earned a bachelor's degree from Wesleyan University where he was an Olin Scholar and where his major was English and his minor Philosophy, and a Juris Doctor (cum laude) from New York University School of Law where he was a Root-Tilden Scholar.