Cognitive control guides behaviour by controlling what, when, and how information is represented in the brain1. For example, attention controls sensory processing; top-down signals from prefrontal and parietal cortex strengthen the representation of task-relevant stimuli2-4. A similar 'selection' mechanism is thought to control the representations held 'in mind'-in working memory5-10. Here we show that shared neural mechanisms underlie the selection of items from working memory and attention to sensory stimuli. We trained rhesus monkeys to switch between two tasks, either selecting one item from a set of items held in working memory or attending to one stimulus from a set of visual stimuli. Neural recordings showed that similar representations in prefrontal cortex encoded the control of both selection and attention, suggesting that prefrontal cortex acts as a domain-general controller. By contrast, both attention and selection were represented independently in parietal and visual cortex. Both selection and attention facilitated behaviour by enhancing and transforming the representation of the selected memory or attended stimulus. Specifically, during the selection task, memory items were initially represented in independent subspaces of neural activity in prefrontal cortex. Selecting an item caused its representation to transform from its own subspace to a new subspace used to guide behaviour. A similar transformation occurred for attention. Our results suggest that prefrontal cortex controls cognition by dynamically transforming representations to control what and when cognitive computations are engaged.