Background: Hypertension is one of the leading risk factors for global mortality, being highly prevalent in low and middle income countries. Among people with chronic illnesses, like hypertension, the burden of depression and anxiety are higher. Presence of depression and anxiety among hypertensive patients lead to lack of adherence to treatment and poor compliance to lifestyle adjustments, which increase patient’s risk of morbidity and mortality. Unlike in high income countries, there is paucity of information on the burden of depression and anxiety among hypertensive patients in low income countries. Objectives: To assess proportion and factors associated with depression and anxiety among hypertensive patients attending selected public hospitals of Addis Ababa, Ethiopia, 2020. Methods: Institution based cross-sectional study was conducted in three randomly selected public hospitals. Through a systematic random sampling, a total of 416 hypertensive patients visiting anti-hypertensive clinics with in the study period of the selected hospitals participated in the study. Data were collected through structured questionnaire administered by an interviewer. Depression and anxiety were assessed through Hospital Anxiety and Depression Scale. The collected data were cleaned, edited and entered in to epi-data version 3.1. Descriptive and bivariable and multivariable logistic analysis were done by using the statistical software, SPSS version 25. Results According to the study, the prevalence of anxiety, depression and comorbid anxiety and depression were found to be 37.8%, 29.5% and 16.5% respectively. Factors found to have significant association with depression were female sex, presence of chronic comorbid illnesses, longer duration of hypertension, current alcohol drinking, family history of depression, marital status and uncontrolled blood pressure. Factors found to have significant association with anxiety were female sex, presence of chronic comorbid illnesses, longer duration of hypertension, current alcohol drinking, retired and non-paid job. Factors which were found to have significant association with comorbid anxiety and depression were female sex, presence of chronic comorbid illnesses, longer duration of hypertension, family history of depression, ever alcohol drinking. Conclusion Higher proportion of depression and anxiety were observed in public health hospitals in Addis Ababa. They are also significantly associated with socio-demographic, clinical and behavioral characteristics. Clinicians should consider mental health status of hypertensive patients.