While the function of most biological systems is tightly constrained by their structure, current evidence suggests that coupling between the structure and function of brain networks is relatively modest. We aimed to investigate whether the modest coupling between connectome structure and function is a fundamental property of nervous systems or a limitation of current brain network models. We developed a new deep learning framework to predict an individual's brain function from their structural connectome, achieving prediction accuracies that substantially exceeded state-of-the-art biophysical models (group: R=0.9±0.1, individual: R=0.55±0.1). Crucially, brain function predicted from an individual's structural connectome explained significant inter-individual variation in cognitive performance. Our results suggest that structure-function coupling in human brain networks is substantially tighter than previously suggested. We establish the margin by which current brain network models can be improved and demonstrate how deep learning can facilitate investigation of relations between brain function and behavior.