Task acquisition in the brain relies on both reward-based and error-based learning (RBL, EBL), yet how the brain brings these two learning signals together remains elusive. Here, we build on the traditional view that dopamine (DA) projections within the basal ganglia (BG) drive RBL via reinforcement learning, while the cerebellum (CB) supports EBL via supervised learning. In doing so, we introduce a novel learning framework that combines DA-driven RBL with CB-driven EBL. Specifically, we reformulate the traditional RBL and EBL synaptic weight updates in terms of a shared ‘action-gradient’ space, which drives plasticity of downstream areas via RBL-EBL (teaching) signals. First, we propose a systems-level implementation of our theory, reflecting the growing evidence of tight BG and CB interactions during learning. Next, we demonstrate the ability of our model to capture several behavioral observations during the acquisition of motor tasks that employ both reward- and error-based learning. Moreover, we show that our model also accounts for well-known motor learning deficits when CB and BG are impaired. Our work provides testable predictions and insights into how and why reward- and error-based learning principles may be combined in the brain.