Mental disorders are among the leading causes of disability worldwide, disproportionately affecting older people. This study aims to assess the mental health of elderly individuals living in a deprived region of Hungary, and to identify and estimate the weight of different determinants of mental health across different age groups. A cross-sectional study was conducted with randomly selected samples of individuals (n = 860) aged 18 years and older in Northeast Hungary. The World Health Organization Well-Being Index (WHO-5), the single-item Life Satisfaction Scale, and the 12-item General Health Questionnaire (GHQ-12) were used to measure mental health of the participants. Multiple linear regression analysis was performed to measure the association between sociodemographic and health-related variables and mental health. Overall, the mean WHO-5 score was 69.2 ± 18.1 and it showed a significant decrease by age (p < 0.001), with the lowest score observed in aged 75 years and above (p < 0.001). The mean life satisfaction score was 7.5 ± 1.9 and it showed a significant decreasing trend over the life course (p < 0.001). The highest level of psychological distress as assessed by GHQ-12 was observed in the group aged 75 years or older (11.5 ± 6.0, p < 0.001). Multiple linear regression indicated that self-reported financial status, social support, sense of control over their health, activity limitation and pain intensity were the most important determinants of mental health among older adults. Interventions to improve the mental health of older adults should focus on the positive impact of social support, the reduction of financial insecurity and the use of effective pain relief medications.