People vary in their ability to learn new motor skills. We hypothesize that between-subject variability in brain structure and function can explain differences in learning. We use brain functional and structural MRI methods to characterize such neural correlates of individual variations in motor learning. Healthy subjects applied isometric grip force of varying magnitudes with their right hands cued visually to generate smoothly-varying pressures following a regular pattern. We tested whether individual variations in motor learning were associated with anatomically colocalized variations in magnitude of functional MRI (fMRI) signal or in MRI differences related to white and grey matter microstructure. We found that individual motor learning was correlated with greater functional activation in the prefrontal, premotor, and parietal cortices, as well as in the basal ganglia and cerebellum. Structural MRI correlates were found in the premotor cortex [for fractional anisotropy (FA)] and in the cerebellum [for both grey matter density and FA]. The cerebellar microstructural differences were anatomically colocalized with fMRI correlates of learning. This study thus suggests that variations across the population in the function and structure of specific brain regions for motor control explain some of the individual differences in skill learning. This strengthens the notion that brain structure determines some limits to cognitive function even in a healthy population. Along with evidence from pathology suggesting a role for these regions in spontaneous motor recovery, our results also highlight potential targets for therapeutic interventions designed to maximize plasticity for recovery of similar visuomotor skills after brain injury.