Fulton studied at the University of Tennessee in Knoxville. Between 1945 and 1946 he served in the United States Navy. From 1958 to 1960 Fulton was a member of the Senate of Tennessee. He was in 1962 elected as a Democrat to the 88th Congress. As a parliamentarian, he was the fifth electoral district of the state of Tennessee from 3 January 1963 until his resignation on 14 August 1975 at the U.S. House of Representatives. During this time he participated in 1964 at the Democratic National Convention in Atlantic City.
This was followed by Fulton Mayor of Nashville. This office he held as a successor of Beverly Briley of 14 August 1975 to 5 October 1987. In the years 1978 and 1986 he applied unsuccessfully to each his party's nomination for the gubernatorial elections.