Atkinson married Susie Cobb Milton in 1880 and their son, William Yates Atkinson, Jr. was the Georgia Democratic state chair in 1942 as well as a Georgia state Supreme Court justice from 1943 to 1948.
The elder Atkinson was the solicitor of the Coweta Superior Court circuit. He then represented Coweta County as a member of the Georgia House of Representatives (1886-94), where he was the speaker, or presiding officer, during the last two years. He was also the Georgia Democratic Party state chair from 1890 to 1892.
Atkinson died on August 8, 1899 in Newnan, Georgia and was buried in Oak Hill Cemetery in that city.
Other notable facts about Atkinson:
- He hired the first woman salaried employee in state government, Ellen Dortch, as assistant state librarian.
- Atkinson County, Georgia is named for him.
- He vetoed a law that would have prohibited football in the state.
- As a state representative, he introduced a bill that established the Georgia Normal and Industrial College, which later became Georgia College and State University in Milledgeville, Georgia.