Background Patient awareness level of anesthesia and anesthetist is not well known in the study area which makes patients blind about the risk and benefits of anesthesia and the role of anesthetists'. This study aimed to assess elective surgical patients' awareness and its associated factors of anesthesia and anesthetists’ in Debre tabor comprehensive specialized Hospital, north-central Ethiopia, 2021. Method Institutional based cross-sectional study was conducted on 367 patients who underwent for elective general surgery in Debre Tabor Comprehensive Specialized Hospital from December 15, 2020, up to May 15, 2021. Data were collected with a structured questionnaire of 13 items after translating the English version to the local language (Amharic). Descriptive statistics were expressed in percentage and presented with tables. Bivariable and multivariable logistic analysis were done to identify factors associated with the awareness level of patients on anesthesia and anesthetists. Statistical significance level was set at P < 0.05 with 95 % CI. Results In this study, 25.1 % [95 % CI= (20.7–29.6)] of patients were adequately aware of anesthesia and anesthetist. Multivariable logistic analyses showed that male patients [AOR = 1.90; 95 % CI= (1.03–3.52)], level of education of secondary school [AOR = 3.20; 95 % CI= (1.07–9.61)] and collage and above [AOR = 4.75; 95 % CI= (1.73–13.06)], patients from Urban [AOR = 6.34; 95 % CI= (3.01–13.39)], and patients with previous anesthesia exposure [AOR = 3.43; 95 % CI= (1.76–6.69)] were more aware of anesthesia and anesthetist than their counterparts. Conclusion The awareness level of patients about anesthesia and anesthetists in this study was poor. Sex, residency, educational level, and previous anesthesia exposure were factors associated with patients’ awareness level of anesthesia and anesthetists.