The white matter architecture of brain networks imparts a distinct signature on neuronal co-activation patterns. Inter-regional projections promote synchrony among distant neuronal populations, giving rise to richly patterned functional networks. A variety of statistical, communication and biophysical models have been proposed to study the relationship between brain structure and function, but the link is not yet known. In the present report we seek to relate the structural and functional connection profiles of individual brain areas. We apply a simple multilinear model that incorporates information about spatial proximity, routing and diffusion between brain regions to predict their functional connectivity. We find that structure-function relationships vary markedly across the neocortex. Structure and function correspond closely in unimodal, primary sensory and motor regions, but diverge in transmodal cortex, corresponding to the default mode and salience networks. The divergence between structure and function systematically follows functional and cytoarchitectonic hierarchies. Altogether, the present results demonstrate that structural and functional networks do not align uniformly across the brain, but gradually uncouple in higher-order polysensory areas.