Born in Montgomery, Alabama, Varner received a Bachelor of Science degree from Auburn University in 1942 and was a United States Naval Aviator Lieutenant (JG) during World War II, from 1942 to 1946.

He received a Juris Doctor from the University of Alabama School of Law in 1949.

He was a member of the Macon County Board of Education from 1950 to 1954, serving as Chairman in 1954.

He was an Assistant United States Attorney of the Middle District of Alabama from 1954 to 1958, returning to private practice in Montgomery from 1958 to 1971.

[1] On February 10, 1971, Varner was nominated by President Richard Nixon to a new seat on the United States District Court for the Middle District of Alabama created by 84 Stat.