Thompson was born in Millen, Georgia to Henry J. And Eva (Edenfield) Thompson. He graduated from Emory University in 1926 and earned a Master of Arts (M.A.) from the University of Georgia in 1935. Thompson worked in education, first as a teacher and coach, a principal, a district superintendent, moving all the way up to assistant school superintendent for the state. Thompson was a supporter of Governor Ellis Arnall and he was his executive secretary and state revenue commissioner.
In 1946, Thompson ran for the newly created position of Lieutenant Governor of Georgia. Arnall supported another candidate. Thompson won the primary with less than thirty percent of the vote.
Governor-elect Eugene Talmadge died in December 1946 and the Georgia state constitution was vague on who would be sworn in to replace him. Thompson felt that as the Lieutenant Governor-elect, he should become the Governor. But the state legislature was controlled by Talmadge supporters. They invoked a clause in the Georgia state constitution which allowed for the legislature to pick between the second and third place candidates. The people who finished second and third were two write-in candidates, James V. Carmichael and Eugene's son, Herman E. Talmadge. The legislature selected Herman Talmadge to become the Governor.
Thompson and Arnall both claimed the office of Governor. Arnall later renounced his claim to support Thompson. The Supreme Court of Georgia ruled that Thompson was the legitimate governor and that the legislature had violated the state constitution by selecting Talmadge. Thompson's achievements as Governor include raising salaries for teachers. He was defeated by Talmadge in a special election in 1948.
Thompson unsuccessfully opposed Talmadge three additional times, twice in gubernatorial elections in 1950 and 1954 and finally in 1956 for one of Georgia's United States Senate seats. Following the Senate campaign defeat, Thompson retired to Valdosta, Georgia where he worked as a realtor. When he died in 1980 at Valdosta he was interred in a mausoleum in the Lakeview Cemetery in that same city.