The cerebellum regulates nonmotor behavior, but the routes by which it exerts its influence are not well characterized. Here we report a necessary role for posterior cerebellum in guiding flexible behavior, acting through a network of diencephalic and neocortical structures. After chemogenetic inhibition of Purkinje cells in lobule VI or crus I, high-throughput automated analysis of complex whole-body movement revealed deficiencies in across-day adaptation to an open field environment. Neither perturbation affected gait, within-day open-field adaptation, or location preference. Mice could learn a water Y-maze task but were impaired in their ability to reverse their initial choice. To map targets of perturbation, we imaged c-Fos activation in cleared whole brains using light-sheet microscopy. Reversal learning activated diencephalic regions and associative neocortical regions. Distinctive subsets of structures were altered by perturbation of lobule VI (thalamus and habenula) and crus I (hypothalamus and prelimbic/orbital cortex), and both perturbations influenced anterior cingulate and infralimbic cortex. Taken together, these experiments reveal parts of a brainwide system for cerebellar influence to guide flexible learning.