Background: Ethiopia has rapidly expanded training programs for associate clinician anesthetists in order to address shortages of anesthesia providers. However, retaining them in the public health sector has proven challenging. This study aimed to determine anesthetists’ intentions to leave their jobs and identify factors that predict turnover intentions. Methods: A nationally representative, cross-sectional survey of 251 anesthetists working in public-sector hospitals in Ethiopia was conducted in 2014. Respondents were asked whether they planned to leave the job in the next year and what factors they considered important when making decisions to quit. Bivariate and multivariable logistic regressions were conducted to investigate 16 potential predictors of turnover intentions, including personal and facility characteristics as well as decision-making factors. Results: Almost half (n = 120; 47.8%) of anesthetists planned to leave their jobs in the next year, and turnover intentions peaked among those with 2–5 years of experience. Turnover intentions were not associated with the compulsory service obligation. Anesthetists rated salary and opportunities for professional development as the most important factors in decisions to quit. Five predictors of turnover intentions were significant in the multivariable model: younger age, working at a district rather than regional or referral hospital, the perceived importance of living conditions, opportunities for professional development, and conditions at the workplace. Conclusions: Human resources strategies focused on improving living conditions for anesthetists and expanding professional development opportunities may increase retention. Special attention should be focused on younger anesthetists and those posted at district hospitals.