Significance Major gaps remain in our understanding of mechanisms that underlie the folding of the human cerebral cortex. Stereotyped folding in specific cortical locations could be explained by a corresponding anatomical pattern of genetic influences on cortical development, but no direct evidence supports this explanation. Here, we use high-resolution brain MRI to show the existence of the predicted pattern of genetic influences on the thickness of the cerebral cortex, leveraging the prediction that shared genetic influences during development create covariability of cortical thickness in adult neuroanatomy. Anatomically local covariability in cortical thickness has a genetic basis, is symmetric between cortical hemispheres, shows consistency across independent datasets, and may influence patterns of surface folding on the human brain.