Born and raised in New Haven, Connecticut, Scully attended Hillhouse High School. At the age of 16, he entered Yale University. He earned his BA degree from Yale in 1940, his M.A. in 1947, and his Ph.D in 1949. He taught classes at Yale from 1947, often to packed lecture rooms. He was also a Distinguished Visiting Professor at the University of Miami. Scully officially retired from Yale in 1991, but continued giving courses there and at the University of Miami. He announced in 2009, however, at the age of 89, that he was no longer well enough to continue teaching.