Born in Coy, Alabama, Godbold received a Bachelor of Science degree from Auburn University in 1940 and was a Major in the United States Army, Division Artillery Headquarters during World War II, from 1941 to 1946.

He received a Juris Doctor from Harvard Law School in 1948, and was in private practice in Montgomery, Alabama from 1948 to 1966.

[1] Godbold was nominated by President Lyndon B. Johnson on June 28, 1966, to a seat on the United States Court of Appeals for the Fifth Circuit vacated by Judge Richard Rives.

He was confirmed by the United States Senate on July 22, 1966, and received his commission the same day.

He served as Chief Judge from February 2, 1981, until he was reassigned by operation of law to the newly formed United States Court of Appeals for the Eleventh Circuit on October 1, 1981.