Microscopic features (that is, microstructure) of axons affect neural circuit activity through characteristics such as conduction speed. To what extent axonal microstructure in white matter relates to functional connectivity (synchrony) between brain regions is largely unknown. Using MRI data in 11,354 subjects, we constructed multivariate models that predict functional connectivity of pairs of brain regions from the microstructural signature of white matter pathways that connect them. Microstructure-derived models provided predictions of functional connectivity that explained 3.5% of cross-subject variance on average (ranging from 1-13%, or r = 0.1-0.36) and reached statistical significance in 90% of the brain regions considered. The microstructure-function relationships were associated with genetic variants, co-located with genes DAAM1 and LPAR1, that have previously been linked to neural development. Our results demonstrate that variation in white matter microstructure predicts a fraction of functional connectivity across individuals, and that this relationship is underpinned by genetic variability in certain brain areas.