Later-life changes in brain tissue volumes—decreases in the volume of healthy grey and white matter and increases in the volume of white matter hyperintensities (WMH)—are strong candidates to explain some of the variation in ageing-related cognitive decline. We assessed Fluid Intelligence, Memory, and Processing Speed, and brain volumes (from structural MRI) at mean age 73 years, and at mean age 76 in a narrow-age sample of older individuals (n = 657 with brain volumetric data at the initial wave, n = 465 at follow-up). We used latent variable modeling to extract error-free cognitive levels and slopes. Initial levels of cognitive ability were predictive of subsequent brain tissue volume changes. Initial brain volumes were not predictive of subsequent cognitive changes. Brain volume changes, especially increases in WMH, were associated with declines in each of the cognitive abilities. All statistically significant results were modest in size (absolute r-values ranged from 0.114 to 0.334). These results build a comprehensive picture of macrostructural brain volume changes and declines in important cognitive faculties during the eighth decade of life.