Background Balance and mobility impairments are important modifiable risk factors associated with falls in older people. Purpose To investigate how different functional fitness components relate to balance and mobility, after controlling for age, sex, body mass index (BMI), and different physical activity (PA) domains. Methods This representative cross-sectional study included 802 individuals, 401 males and 401 females (69.8 ± 5.6 years) from Madeira, Portugal. The Fullerton Advance Balance (FAB) scale was used to assess balance. Mobility in terms of gait velocity, cadence, stride length, and gait stability ratio (GSR) were assessed using the 50-foot Walk test. PA was assessed through a face-to-face interview using the Baecke questionnaire, and functional fitness was assessed with Senior Fitness tests (strength, flexibility, and aerobic endurance). Results Balance and mobility were negatively associated with age and BMI, and positively related to PA and functional fitness. Moreover, male presented better performance in balance and mobility. Hierarchical multiple regression analyses showed that functional fitness explained the highest amount of variance in balance and all mobility parameters (over and above age, sex, BMI, and PA). Specifically, entering functional fitness components significantly increased explained variance in FAB (+19%), gait velocity (+25%), cadence (+15%), stride length (+9%), and GSR (+ 31%). In these models, aerobic endurance consistently had the strongest contribution. Conclusion Strength, flexibility, and especially aerobic endurance, over and above non-modifiable variables like age and sex, are crucial for maintaining or improving balance and mobility and, thereby, prevent falls in older people.