Alzheimer’s disease is currently the leading cause of dementia and one of the most expensive, lethal and severe diseases worldwide. Age-related decline in executive function is widespread and plays a key role in subsequent dementia risk. Physical exercise has been proposed as one of the leading non-pharmaceutical approaches to improve executive function and ameliorate cognitive decline. This single-site, two-arm, single-blinded, randomized controlled trial (RCT) will include 90 cognitively normal older adults, aged 65–80 years old. Participants will be randomized to a 24-week resistance exercise program (3 sessions/week, 60 min/session, n = 45), or a wait-list control group (n = 45) which will be asked to maintain their usual lifestyle. All study outcomes will be assessed at baseline and at 24-weeks after the exercise program, with a subset of selected outcomes assessed at 12-weeks. The primary outcome will be indicated by the change in an executive function composite score assessed with a comprehensive neuropsychological battery and the National Institutes of Health Toolbox Cognition Battery. Secondary outcomes will include changes in brain structure and function and amyloid deposition, other cognitive outcomes, and changes in molecular biomarkers assessed in blood, saliva, and fecal samples, physical function, muscular strength, body composition, mental health, and psychosocial parameters. We expect that the resistance exercise program will have positive effects on executive function and related brain structure and function, and will help to understand the molecular, structural, functional, and psychosocial mechanisms involved.