Physical and cognitive training can maintain and improve older adults’ independence and quality of life. Given the demographic growth of the older adult population and the shortage of caregivers, there is a need for personal trainers for physical and cognitive activities. This study suggests that social robots can satisfy this demand and presents the development of “Gymmy”, a robotic system for the physical and cognitive training of older adults. The system design includes a humanoid mechanical-looking robot to demonstrate exercises, an RGB-Depth (RGB-D) camera to measure performance and a touch screen and speakers to provide instructions and feedback. Experiments with 26 older adults (65–84 years of age) were performed in home environments to examine the effect of users’ characteristics (age, gender, education and attitude toward robots), the addition of cognitive training and the success rate of the acceptability of a robot trainer. The results showed that age, attitude and education influenced the acceptance of the robotic system. The findings highlight the importance of customizing the system to the needs of different users and the role of meaningful feedback. The system was proven to be robust and reliable, demonstrating clear potential to be used as a personal trainer and as a means of motivating older adults.