The population of the world is aging and one of the main concerns of the aged care industry is to provide appropriate care for elderly people as their health and independent functioning declines. This paper reports a systematic review of the roll of Socially Assistive Robots (SAR) in elderly wellbeing, based on Cochrane principles. Relevant publications from diverse databases, including healthcare, engineering, and robotics were sourced and screened. Ninety-five studies in forty-two study groups have been synthesized. The reported outcomes have been categorized based on five PERMA constructs (Positive emotion, Engagement, Relationships, Meaning, and Achievement) in addition to a sixth category (other effects). The findings indicate that SAR has the potential to enhance elderly wellbeing and decrease the workload of caregivers. Based on concerns that emerged during the quality appraisal process, several significant recommendations are made to improve future research and its applicability. Furthermore, acknowledging individuals’ needs, expectations, and preferences alongside multi-modal interaction and data collection translates into improvement of personalization of care. The development of new approaches such as web-based interf aces and cloud computing are highly recommended as the means of overcoming the constraints of the limited computing and storage capabilities of SAR. Moreover, human-like engagement characteristics of socially assistive robots should be seamlessly integrated with other assistive technologies such as tele-health, e-health, and smart homes.