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Cognition is remarkably flexible; we are able to rapidly learn and perform many different tasks 1 . Theoretical modeling has shown artificial neural networks trained to perform multiple tasks will re-use representations 2 and computational components 3 across tasks. By composing tasks from these sub-components, an agent can flexibly switch between tasks and rapidly learn new tasks 4 . Yet, whether such compositionality is found in the brain is unknown. Here, we show the same subspaces of neural activity represent task-relevant information across multiple tasks, with each task compositionally combining these subspaces in a task-specific manner. We trained monkeys to switch between three compositionally related tasks. Neural recordings found task-relevant information about stimulus features and motor actions were represented in subspaces of neural activity that were shared across tasks. When monkeys performed a task, neural representations in the relevant shared sensory subspace were transformed to the relevant shared motor subspace. Subspaces were flexibly engaged as monkeys discovered the task in effect; their internal belief about the current task predicted the strength of representations in task-relevant subspaces. In sum, our findings suggest that the brain can flexibly perform multiple tasks by compositionally combining task-relevant neural representations across tasks., Competing Interests: Competing Interests The authors declare no competing interests.