Postmortem histological studies have demonstrated that myelination in human brain white matter (WM) continues throughout adolescence and well into adulthood. We used in vivo diffusion-weighted magnetic resonance imaging to test for age-related WM changes in 42 adolescents and 20 young adults. Tract-Based Spatial Statistics (TBSS) analysis of the adolescent data identified widespread age-related increases in fractional anisotropy (FA) that were most significant in clusters including the body of the corpus callosum and right superior corona radiata. These changes were driven by changes in perpendicular, rather than parallel, diffusivity. These WM clusters were used as seeds for probabilistic tractography, allowing us to identify the regions as belonging to callosal, corticospinal, and prefrontal tracts. We also performed voxel-based morphometry-style analysis of conventional T1-weighted images to test for age-related changes in grey matter (GM). We identified a cluster including right middle frontal and precentral gyri that showed an age-related decrease in GM density through adolescence and connected with the tracts showing age-related WM FA increases. The GM density decrease was highly significantly correlated with the WM FA increase in the connected cluster. Age-related changes in FA were much less prominent in the young adult group, but we did find a significant age-related increase in FA in the right superior longitudinal fascicle, suggesting that structural development of this pathway continues into adulthood. Our results suggest that significant microstructural changes in WM continue throughout adolescence and are associated with corresponding age-related changes in cortical GM regions.