Functional brain networks require dynamic reconfiguration to support flexible cognitive function. However, the developmental principles shaping brain network dynamics remain poorly understood. Here, we report the longitudinal development of large-scale brain network dynamics during childhood and adolescence, and its connection with gene expression profiles. Using a multilayer network model, we show the temporally varying modular architecture of child brain networks, with higher network switching primarily in the association cortex and lower switching in the primary regions. This topographical profile exhibits progressive maturation, which manifests as reduced modular dynamics, particularly in the transmodal (e.g., default-mode and frontoparietal) and sensorimotor regions. These developmental changes mediate age effects on network communication efficiency and are connected with the expression profile of genes associated with the enrichment of ion transport and nucleobase-containing compound transport. These results highlight a progressive stabilization of brain dynamics, which expand our understanding of the neural mechanisms that underlie cognitive development.