Behavioural feedback is critical for learning in the cerebral cortex, but such feedback is often not readily available which slows down learning. Inspired by deep learning algorithms, we introduce a systems-level computational model of cerebro-cerebellar interactions in which a cerebral recurrent network receives continuous cerebral feedback predictions from a cerebellar network, thereby decoupling learning in cerebral networks from future feedback. When trained in a simple sensorimotor task the model shows faster learning and reduced ataxia-like behaviours, in line with experimental observations. Next, we demonstrate that these results generalise to a range of more complex motor and cognitive tasks. Finally, we highlight a number of experimentally testable predictions regarding (1) how cerebral and cerebellar representations develop over learning, (2) how cerebral and task feedback properties shape the need for cerebellar predictions and (3) the differential impact of lesions of the cerebellar output and inferior olive. Overall, our work offers a novel theoretical framework of cerebro-cerebellar networks as feedback decoupling machines.