The duplication of chromosome 21, as evidenced in Down Syndrome (DS), has been linked to contraindications to health, such as chronotropic and respiratory incompetence, neuromuscular conditions, and impaired cognitive functioning. The purpose of this study was to examine the effects of eight weeks of prescribed exercise and/or cognitive training on the physical and cognitive health of adults with DS. Eighty-three participants (age 27.1 ± 8.0 years) across five continents participated. Physical fitness was assessed using a modified version of the six-minute walk test (6MWT), while cognitive and executive functions were assessed using the Corsi block test, the Sustained-Attention-To-Response Task (SART), and the Stroop task (STROOP). All were completed pre- and post-intervention. Participants were assigned to eight weeks of either exercise (EXE), 3 × 30 min of walking/jogging per week, cognitive training (COG) 6 × ~20 min per week, a combined group (COM), and a control group (CON) engaging in no intervention. 6MWT distance increased by 11.4% for EXE and 9.9% for COM (p < 0.05). For SART, there were positive significant interactions between the number of correct and incorrect responses from pre- to post-intervention when participants were asked to refrain from a response (NO-GO-trials) across all experimental groups (p < 0.05). There were positive significant interactions in the number of correct, incorrect, and timeout incompatible responses for STROOP in EXE, COG, and COM (p < 0.05). Walking generated a cognitive load attributed to heightened levels of vigilance and decision-making, suggesting that exercise should be adopted within the DS community to promote physical and cognitive well-being.