The white matter (WM) architecture of the human brain changes in response to training, though fine-grained temporal characteristics of training-induced white matter plasticity remain unexplored. We investigated white matter microstructural changes using diffusion tensor imaging at five different time points in 26 sighted female adults during 8 months of training on tactile braille reading. Our results show that training-induced white matter plasticity occurs both within and beyond the trained sensory modality, as reflected by fractional anisotropy (FA) increases in somatosensory and visual cortex, respectively. The observed changes followed distinct time courses, with gradual linear FA increase along the training in the somatosensory cortex and sudden visual cortex cross-modal plasticity occurring after braille input became linguistically meaningful. WM changes observed in these areas returned to baseline after the cessation of learning in line with the supply-demand model of plasticity. These results also indicate that the temporal dynamics of microstructural plasticity in different cortical regions might be modulated by the nature of computational demands. We provide additional evidence that observed FA training-induced changes are behaviorally relevant to tactile reading. Together, these results demonstrate that WM plasticity is a highly dynamic process modulated by the introduction of novel experiences.SIGNIFICANCE STATEMENT Throughout the lifetime the human brain is shaped by various experiences. Training-induced reorganization in white matter (WM) microstructure has been reported, but we know little about its temporal dynamics. To fill this gap, we scanned sighted subjects five times during tactile braille reading training. We observed different dynamics of WM plasticity in the somatosensory and visual cortices implicated in braille reading. The former showed a continuous increase in WM tissue anisotropy along with tactile training, while microstructural changes in the latter were observed only after the participants learned to read braille words. Our results confirm the supply-demand model of brain plasticity and provide evidence that WM reorganization depends on distinct computational demands and functional roles of regions involved in the trained skill.