Fitts was a severely injured veteran of World War I whose base of political support lay in the American Legion organization of war veterans. He had been shot in the knee in the Battle of Argonne and limped for the rest of his life.
He was appointed deputy district attorney for Los Angeles County in 1920 during the term of Thomas Lee Woolwine and chief deputy in 1924 under Asa Keyes. He was elected lieutenant governor in 1926 and served in the administration of Governor C.C. Young. Fitts term as lieutenant governor of California: January 4, 1927 to November 30, 1928. Governor Young appointed H. L. Carnahan, lieutenant governor on December 4, 1928, vice Buron Fitts, resigned.
In 1928, Keyes was indicted for bribery (in connection with the Julian Petroleum Company scandal), and Fitts resigned effective November 30 of that year to become a special prosecutor in that case. He was elected district attorney (the county's chief law officer) as well.
Fitts was elected for a second term in 1932, and he investigated the death of Hollywood producer-director-screenwriter Paul Bern, the husband of actress Jean Harlow. Samuel Marx, in his book Deadly Illusions (1990) accuses Fitts of having been bribed by MGM studio officials to accept a fabricated version of Bern's suicide to avoid scandal in Hollywood. Fitts was also indicted for bribery, and perjury in 1934 for allegedly taking a bribe to drop a statutory rape charge against a millionaire real-estate promoter. He was acquitted two years later. He was also accused of using his position to block action against the rapist of Patricia Douglas at the MGM Sales Convention in 1937, a case that was the subject of David Stenn's 2007 documentary film Girl 27.
Fitts was elected to a third term as district attorney in 1936 and remained until 1940, when he was defeated by a reform candidate, John F. Dockweiler. Fitts, J.D. Fredricks (1903–1915), and Steve Cooley (2000-2012) are only Los Angeles County District Attorneys to serve three complete terms.
On March 7, 1937, Fitts was wounded by a volley of shots fired through the windshield of his car. Nobody was ever arrested in that case.
He joined the Army Air Corps in 1942 with the rank of major. He was chief, intelligence, Pacific Overseas Air Technical Services.
- For the People — Inside the Los Angeles County District Attorney's Office 1850-2000 (2001) by Michael Parrish. ISBN 1-883318-15-7
- He Usually Lived With a Female: The Life of a California Newspaperman (2006) by George Garrigues. Quail Creek Press. ISBN 0-9634830-1-3
- Deadly Illusions by Samuel Marx and Joyce Vanderveen (Random House, New York, 1990), re-published as Murder Hollywood Style - Who Killed Jean Harlow's Husband? (Arrow, 1994, ISBN 0-09-961060-4)