Human brain structure topography is thought to be related in part to functional specialisation. However, the extent of such relationships is unclear. Here, using a data-driven, multi-modal approach for studying brain structure across the lifespan (n=484, 260 females), we demonstrate that numerous structural networks, covering the entire brain, follow a functionally-meaningful architecture. These grey matter networks emerge from the co-variation of grey matter volume and cortical area at the population level. We further reveal fine-grained anatomical signatures of functional connectivity. For example, within the cerebellum, a structural separation emerges between lobules that are functionally connected to distinct, mainly sensorimotor, cognitive and limbic regions of the cerebral cortex and subcortex. Structural modes of variation also replicate the fine-grained functional architecture seen in 8 well-defined visual areas in both task and resting-state fMRI. Furthermore, our study shows a structural distinction corresponding to the established segregation between anterior and posterior default-mode networks. These fine-grained grey matter networks further cluster together to form functionally-meaningful larger-scale organisation. In particular, we identify a structural architecture bringing together the functional posterior default-mode network and its anti-correlated counterpart. In summary, our results demonstrate that the relationship between structural and functional connectivity is fine-grained, widespread across the entire brain, and driven by co-variation in cortical area, i.e. likely differences in shape, depth or number of foldings. These results suggest that neurotrophic events occur during development to dictate that the size and folding pattern of distant, functionally-connected brain regions should vary together across subjects.SIGNIFICANCE STATEMENTQuestions over the relationship between structure and function in the human brain have engaged neuroscientists for centuries in a debate that continues to this day. Here, by interrogating inter-subject variation in brain structure across a large number of individuals, we reveal modes of structural variation that map onto fine-grained functional organisation across the entire brain, and specifically in the cerebellum, visual areas and default-mode network. This functionally-meaningful structural architecture emerges from the co-variation of grey matter volume and cortical folding. These results suggest that the neurotrophic events at play during development, and possibly evolution, which dictate that the size and folding pattern of distant brain regions should vary together across subjects, might also play a role in functional cortical specialisation.