Decision-making requires flexibility to rapidly switch one's actions in response to sensory stimuli depending on information stored in memory. We identified cortical areas and neural activity patterns underlying this flexibility during virtual navigation, where mice switched navigation toward or away from a visual cue depending on its match to a remembered cue. Optogenetics screening identified V1, posterior parietal cortex (PPC), and retrosplenial cortex (RSC) as necessary for accurate decisions. Calcium imaging revealed neurons that can mediate rapid navigation switches by encoding a mixture of a current and remembered visual cue. These mixed selectivity neurons emerged through task learning and predicted the mouse's choices by forming efficient population codes before correct, but not incorrect, choices. They were distributed across posterior cortex, even V1, and were densest in RSC and sparsest in PPC. We propose flexibility in navigation decisions arises from neurons that mix visual and memory information within a visual-parietal-retrosplenial network.