Different brain regions can be grouped together, based on cross-sectional correlations among their cortical characteristics; this patterning has been used to make inferences about ageing processes. However, cross-sectional brain data conflates information on ageing with patterns that are present throughout life. We characterised brain cortical ageing across the 8th decade of life in a longitudinal ageing cohort, at ages ~73, ~76, and ~79 years, with a total of 1,376 MRI scans. Volumetric changes among cortical regions of interest (ROIs) were more strongly correlated (average r = 0.805, SD = 0.252) than were cross-sectional volumes of the same ROIs (average r = 0.350, SD = 0.178). We identified a broad, cortex-wide, dimension of atrophy that explained 66% of the variance in longitudinal changes across the cortex. Our modelling also discovered more specific fronto-temporal and occipito-parietal dimensions, that were orthogonal to the general factor and together explained an additional 20% of the variance. The general factor was associated with declines in general cognitive ability (r = 0.431, p < 0.001) and in the domains of visuospatial ability (r = 0.415, p = 0.002), processing speed (r = 0.383, p < 0.001) and memory (r = 0.372, p < 0.001). Individual differences in brain cortical atrophy with ageing are manifest across three broad dimensions of the cerebral cortex, the most general of which is linked with cognitive declines across domains. Longitudinal approaches are invaluable for distinguishing lifelong patterns of brain-behaviour associations from patterns that are specific to aging.