A diverse white matter network and finely tuned neuronal membrane properties allow the brain to transition seamlessly between cognitive states. However, it remains unclear how static structural connections guide the temporal progression of large-scale brain activity patterns in different cogni- tive states. Here, we deploy an unsupervised machine learning algorithm to define brain states as time point level activity patterns from functional magnetic resonance imaging data acquired dur- ing passive visual fixation (rest) and an n-back working memory task. We find that brain states are composed of interdigitated functional networks and exhibit context-dependent dynamics. Using diffusion-weighted imaging acquired from the same subjects, we show that structural connectivity constrains the temporal progression of brain states. We also combine tools from network control theory with geometrically conservative null models to demonstrate that brains are wired to sup- port states of high activity in default mode areas, while requiring relatively low energy. Finally, we show that brain state dynamics change throughout development and explain working mem- ory performance. Overall, these results elucidate the structural underpinnings of cognitively and developmentally relevant spatiotemporal brain dynamics.