Abstract Sleep consolidates memory for procedural motor skills, reflected by sleep-dependent changes in the hippocampal-striatal-cortical network. Other forms of procedural skills require the acquisition of a novel strategy to solve a problem, which recruit overlapping brain regions and specialized areas including the caudate and prefrontal cortex. Sleep preferentially benefits strategy and problem-solving skills over the accompanying motor execution movements. However, it is unclear how acquiring new strategies benefit from sleep. Here, participants performed a task requiring the execution of a sequence of movements to learn a novel cognitive strategy. Participants performed this task while undergoing fMRI before and after an interval of either a full night sleep, a daytime nap, or wakefulness. Participants also performed a motor control task, which precluded the opportunity to learn the strategy. In this way, we subtracted motor execution-related brain activations from activations specific to the strategy. The sleep and nap groups experienced greater behavioral performance improvements compared to the wake group on the strategy-based task. Following sleep, we observed enhanced activation of the caudate in addition to other regions in the hippocampal-striatal-cortical network, compared to wakefulness. This study demonstrates that sleep is a privileged time to enhance newly acquired cognitive strategies needed to solve problems.