Motor adaptation to perturbations is provided by learning mechanisms operating in the cerebellum and basal ganglia. The cerebellum normally performs motor adaptation through supervised learning using information about movement error provided by visual feedback. However, if visual feedback is critically distorted, the system may disengage cerebellar error-based learning and switch to reinforcement learning mechanisms mediated by basal ganglia. Yet, the exact conditions and mechanisms of cerebellum and basal ganglia involvement in motor adaptation remain unknown. We use mathematical modeling to simulate control of planar reaching movements that relies on both error-based and non-error-based learning mechanisms. We show that for learning to be efficient only one of these mechanisms should be active at a time. We suggest that switching between the mechanisms is provided by a special circuit that effectively suppresses the learning process in one structure and enables it in the other. To do so, this circuit modulates learning rate in the cerebellum and dopamine release in basal ganglia depending on error-based learning efficiency. We use the model to explain and interpret experimental data on error- and non-error-based motor adaptation under different conditions.