Late human development is characterized by the maturation of high-level functional processes, which rely on reshaping of white matter connections, as well as synaptic density. However, the relationship between the whole-brain dynamics and the underlying white matter networks in neurodevelopment is largely unknown. In this study, we focused on how the structural connectome shapes the emerging dynamics of cerebral development between the ages of 6 and 33 years, using functional and diffusion magnetic resonance imaging combined into a spatiotemporal connectivity framework. We defined two new measures of brain dynamics, namely the system diversity and the spatiotemporal diversity, which quantify the level of integration/segregation between functional systems and the level of temporal self-similarity of the functional patterns of brain dynamics, respectively. We observed a global increase in system diversity and a global decrease and local refinement in spatiotemporal diversity values with age. In support of these findings, we further found an increase in the usage of long-range and inter-system white matter connectivity and a decrease in the usage of short-range connectivity with age. These findings suggest that dynamic functional patterns in the brain progressively become more integrative and temporally self-similar with age. These functional changes are supported by a greater involvement of long-range and inter-system axonal pathways.