AbstractUnderstanding the neurodegenerative mechanisms underlying cognitive decline in the general population may facilitate early detection of adverse health outcomes in late life. This study investigates genetic links between brain morphometry, ageing and cognitive ability. We develop Genomic Principal Components Analysis (Genomic PCA) to model general dimensions of brain‐wide morphometry at the level of their underlying genetic architecture. Genomic PCA is applied to genome‐wide association data for 83 brain‐wide volumes (36,778 UK Biobank participants) and we extract genomic principal components (PCs) to capture global dimensions of genetic covariance across brain regions (unlike ancestral PCs that index genetic similarity between participants). Using linkage disequilibrium score regression, we estimate genetic overlap between those general brain dimensions and cognitive ageing. The first genetic PCs underlying the morphometric organisation of 83 brain‐wide regions accounted for substantial genetic variance (R² = 40%) with the pattern of component loadings corresponding closely to those obtained from phenotypic analyses. Genetically more central regions to overall brain structure ‐ specifically frontal and parietal volumes thought to be part of the central executive network ‐ tended to be somewhat more susceptible towards age (r = −0.27). We demonstrate the moderate genetic overlap between the first PC underlying each of several structural brain networks and general cognitive ability (r_g = 0.17–0.21), which was not specific to a particular subset of the canonical networks examined. We provide a multivariate framework integrating covariance across multiple brain regions and the genome, revealing moderate shared genetic etiology between brain‐wide morphometry and cognitive ageing.