The spatial distribution of large-scale functional networks on the cerebral cortex differs between individuals and is particularly variable in association networks that are responsible for higher-order cognition. However, it remains unknown how this functional topography evolves in development and supports cognition. Capitalizing on advances in machine learning and a large sample imaged with 27 min of high-quality functional MRI (fMRI) data (n = 693, ages 8–23 years), we delineate how functional topography evolves during youth. We found that the functional topography of association networks is refined with age, allowing accurate prediction of unseen individuals’ brain maturity. The cortical representation of association networks predicts individual differences in executive function. Finally, variability of functional topography is associated with fundamental properties of brain organization, including evolutionary expansion, cortical myelination, and cerebral blood flow. Our results emphasize the importance of considering the plasticity and diversity of functional neuroanatomy during development and suggest advances in personalized therapeutics.