Older people in institutional care are, for the most part, physically inactive and do not interact with each other or medical staff. Therefore, reducing sedentary behaviour is a new, important, and modifiable lifestyle variable that can improve the health of elderly people. The aim of the project was to assess the degree of improvement in functional performance and the possibility of changing habitual, free time behaviour among elderly people under institutional care by applying physical training with verbal stimulation. The study covered older people, aged 65–85 years, who are living a sedentary lifestyle in care homes in Southeastern Poland. Those who met the eligibility criteria were enrolled in the study and were assigned, at random, to one of four parallel groups: basic exercises (n = 51), basic exercises combined with verbal stimulation (n = 51), functional exercise training (n = 51), and functional exercise training with verbal stimulation (n = 51). No statistically significant differences in baseline characteristics were observed across the groups. Data were collected at baseline and at 12 and 24-weeks following the completion of the intervention. In the group with functional exercise training with verbal stimulation, in comparison to the group with basic exercises, the greatest positive short-term impact of intervention was demonstrated in terms of functional fitness (increased by 1.31 points; 95% confidence interval (CI) = 0.93–1.70), gait speed (improved by 0.17 m/s, 95% CI = 0.13–0.22), hand grip strength (by over 4 kg; 95% CI = 2.51–4.95), and upper-limb flexibility (by 10 cm; 95% CI = 5.82–12.65). There was also a significant increase in the level of free-time physical activity and an improvement in the quality of life, especially as expressed in the domain of overall physical functioning. Our study showed that a functional exercise program, combined with verbal stimulation, is effective at improving physical fitness and raising the level of free-time physical activity.