Executive control is a higher‐level cognitive function that involves a range of different processes that are involved in the planning, coordination, execution, and inhibition of responses. Many of the processes associated with executive control, such as response inhibition and mental flexibility, decline with age. Degeneration of white matter architecture is considered to be the one of the key factors underlying cognitive decline associated with aging. Here we investigated how white matter changes of the corpus callosum were related to cognitive aging in common marmosets (Callithrix jacchus). We hypothesized that reduction in myelin thickness, myelin density, and myelin fraction of axonal fibers in the corpus callosum would be associated with performance on a task of executive function in a small sample of geriatric marmosets (n = 4) and young adult marmosets (n = 2). Our results indicated declines in myelin thickness, density, and myelin fraction with age. Considerable variability was detected on these characteristics of myelin and cognitive performance assessed via the detoured reach task. Age‐related changes in myelin in Region II of the corpus callosum were predictive of cognitive performance on the detoured reach task. Thus the detoured reach task appears to also measure aspects of corticostriatal function in addition to prefrontal cortical function.