This study looks at the effects of exercise programs on physical factors and safety in adult patients with cancer and hematopoietic stem cell transplantation (HSCT) or bone marrow transplantation (BMT). A systematic search was performed in the PubMed and Web of Science databases (from inception to 26 August 2021). A review was carried out following the Preferred Reporting Items for Systematic review and Meta-Analyses (PRISMA) checklist. The methodological quality of the included studies was assessed with the Physiotherapy Evidence Database (PEDro) scale, based, in turn, on the Delphi list. A total of 25 randomized controlled trials studies were included, comprising 1434 patients. The most significant result of this systematic review is that exercise program interventions are safe and produce positive changes in cardiorespiratory fitness, muscle strength, and the functional mobility-state in adult patients with cancer and HSCT or BMT. Only 3 patients from the 711 participants in the exercise interventions (i.e., 0.42%) reported adverse events related to exercise interventions. Moreover, exercise training programs may have a cardiological and muscular protective effect, as well as a healthy effect on the prevention and control of transplant complications, improving health outcomes.