Sensorimotor function is a fundamental brain function in humans, and the cerebrocerebellar circuit is essential to this function. In this study, we demonstrate how the cerebrocerebellar circuit develops both functionally and anatomically from childhood to adulthood in the typically developing human brain. We measured brain activity using functional magnetic resonance imaging while a total of 57 right-handed, blindfolded, healthy children (aged 8–11 years), adolescents (aged 12–15 years), and young adults (aged 18–23 years) (n = 19 per group) performed alternating extension–flexion movements of their right wrists in precise synchronization with 1-Hz audio tones. We also collected their diffusion MR images to examine the extent of fiber maturity in cerebrocerebellar afferent and efferent tracts by evaluating the anisotropy-sensitive index of hindrance modulated orientational anisotropy (HMOA). During the motor task, although the ipsilateral cerebellum and the contralateral primary sensorimotor cortices were consistently activated across all age groups, the functional connectivity between these two distant regions was stronger in adults than in children and adolescents, whereas connectivity within the local cerebellum was stronger in children and adolescents than in adults. The HMOA values in cerebrocerebellar afferent and efferent tracts were higher in adults than in children (some were also higher than in adolescents). The results indicate that adult-like cerebrocerebellar functional coupling is not completely achieved during childhood and adolescence, even for fundamental sensorimotor brain function, probably due to anatomical immaturity of cerebrocerebellar tracts. This study clearly demonstrated the principle of “local-to-distant” development of functional brain networks in the human cerebrocerebellar sensorimotor network.