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Across healthy adult life our brains undergo gradual structural change in a pattern of atrophy that resembles accelerated brain changes in Alzheimer's disease (AD). Here, using four polygenic risk scores for AD (PRS-AD) in a longitudinal adult lifespan sample aged 30 to 89 years (2-7 timepoints), we show that healthy individuals who lose brain volume faster than expected for their age, have a higher genetic AD risk. We first demonstrate PRS-AD associations with change in early Braak regions, namely hippocampus, entorhinal cortex, and amygdala, and find evidence these extend beyond that predicted by APOE genotype. Next, following the hypothesis that brain changes in ageing and AD are largely shared, we performed machine learning classification on brain change trajectories conditional on age in longitudinal AD patient-control data, to obtain a list of AD-accelerated features and model change in these in adult lifespan data. We found PRS-AD was associated with a multivariate marker of accelerated change in many of these features in healthy adults, and that most individuals above ~50 years of age are on an accelerated change trajectory in AD-accelerated brain regions. Finally, high PRS-AD individuals also high on a multivariate marker of change showed more adult lifespan memory decline, compared to high PRS-AD individuals with less brain change. Our results support a dimensional account linking normal brain ageing with AD, suggesting AD risk genes speed up the shared pattern of ageing- and AD-related neurodegeneration that starts early, occurs along a continuum, and tracks memory change in healthy adults.