The purpose of this study was to determine (a) the effects of strength training (ST) on physical function and (b) the influence of strength, power, muscle volume (MV), and body composition on physical function. Healthy, inactive adults (n = 50) aged 65 years and older underwent strength, power, total body composition (% fat and fat free mass [FFM]), and physical function testing before and after 22 weeks of ST. Physical function testing consisted of tasks designed to mimic common physical activities of daily living (ADL). To improve internal validity of the assessment of mid-thigh intermuscular fat, subcutaneous fat, and knee extensors MV, a 10-week unilateral ST program using the untrained leg as an internal control preceded 12 weeks of whole-body ST. Strength, power, and FFM increased significantly with ST (all p < 0.05), whereas rapid walk, 5 chair stands, and get up and go time decreased significantly with ST in the overall group (all p < 0.05). Women improved significantly in both walking test times (both p < 0.05) but not in the stair climb test, whereas men improved in the stair climb test (p < 0.05) but not in walking test times. Multiple regression analysis revealed the highest R (0.28) for the change in chair stands time, followed by stair climb and usual walk at 0.27 and 0.21, respectively. ST improves performance in functional tasks important for ADLs. Changes in strength, power, and FFM are predictors of ST-induced improvements in these tasks.