SummaryDuring task execution cortical dynamics must bridge sensory cues with future behavioural outcomes. However, how cortical networks acquire such task-specific dynamics remains unclear. Here we propose that the cerebellum drives cortical dynamics to enable rapid and flexible task acquisition. We model cerebellar networks that are tuned through timing rules to provide cortical networks with task-outcome predictions. First, using sensorimotor tasks we show that cerebellar feedback with fixed cortical connectivity is sufficient for rapid task acquisition and one-shot task switching. Next, we demonstrate that, when trained in working memory tasks, the cerebellum can also underlie the maintenance of cognitive-specific dynamics, explaining a range of optogenetic and behavioural observations. Finally, we use our model to introduce a systems consolidation theory in which task information is gradually transferred from the cerebellum to the cortex. In summary, our results suggest that cortico-cerebellar loops are critical for task acquisition, switching and consolidation in the brain.