Davis has served as mayor the northwest Mississippi city for 16 years.
Davis says in a statement released Thursday that he reached the decision after talking with his partner and family.
The 46-year-old Davis, who admitted he was gay more than a year ago, cited a long list of accomplishments during his tenure in the release. He did not mention his legal problems as a factor.
State Auditor Stacey Pickering has ordered Davis to repay more than $170,000 including penalties and interest that Pickering said was misspent from city funds.
Davis was indicted in December on state charges of making false statements related to a car purchase, city gas and a check from a city account.