We performed a randomized, controlled trial to analyse the effects of resistance training (RT) on cognitive and physical function among older adults. Fifty participants (mean age 67 years, ~60% woman) were randomly assigned to an RT program or a control group. Participants allocated to RT performed three sets of 10-15RM in nine exercises, three times per week, for 12-weeks. Control group did not perform any exercise. Variables included cognitive (global and executive function) and physical function (gait, mobility and strength) outcomes. At completion of the intervention, RT was shown to have significantly mitigated the drop in selective attention and conflict resolution performance (Stroop test: -494.6; 95%CI: -883.1; −106.1) and promoted a significant improvement in working memory (digit span forward: -0.6; 95%CI: −1.0; −0.1 and forward minus backward: -0.9; 95% CI: −1.6; −0.2) and verbal fluency (animal naming: +1.4, 95%CI 0.3, 2.5). No significant between-group differences were observed for other cognitive outcomes. Regarding physical function, at completion of the intervention, the RT group demonstrated improved fast-pace gait performance (−0.3; 95% CI: −0.6; −0.0) and 1-RM (+21.4 kg; 95%CI: 16.6; 26.2). No significant between-group differences were observed for other mobility-related outcomes. In conclusion, RT improves cognitive and physical function of older adults.