The aim of the present study was to understand the effect of a multicomponent physical exercise program on the functional physical fitness of older people with overweight or obesity in Chile, and whether these effects were similar in women and men. For this purpose, a quasi-experimental study was designed with a control group to evaluate the functional physical fitness through the Senior Fitness Test battery for older people [SFT; aerobic endurance (AE), lower body strength (LBS), upper body strength (UBS), upper body flexibility (UBF), lower body flexibility (LBF), dynamic balance (DB), and hand pressure strength right (HPSR) and left (HPSL)]. Seventy older people with overweight or obesity aged between 60 and 86 years participated (M = 73.15; SD = 5.94), and were randomized into a control group (CG, n = 35) and an experimental group (EG, n = 35). The results after the intervention between the CG and EG indicated that there were statistically significant differences in the AE (p = 0.036), in the LBS (p = 0.031), and in the LBF (p = 0.017), which did not exist before the intervention (p > 0.050), except in the HPSR (0.029). Regarding the results of the EG (pre vs. post-intervention), statistically significant differences were found in all of the variables studied: AE (p < 0.001), LBS (p < 0.001), UBS (p < 0.001), LBF (p = 0.017), UBF (p < 0.001), DB (p = 0.002), HPSR (p < 0.001), and HPSL (p = 0.012) in both men and women. These improvements did not exist in any of the CG variables (p > 0.05). Based on the results obtained, we can say that a multicomponent physical exercise program applied for 6 months in older people with overweight or obesity produces improvements in functional physical fitness regardless of sex, except in lower body flexibility and left-hand dynamometry.