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Abstract INTRODUCTION While studies report that sleep disturbance can have negative effects on brain vasculature, its impact on cerebrovascular diseases such as white matter hyperintensities (WMHs) in beta‐amyloid‐positive older adults remains unexplored. METHODS Sleep disturbance, WMH burden, and cognition in normal controls (NCs), and individuals with mild cognitive impairment (MCI) and Alzheimer's disease (AD), were examined at baseline and longitudinally. A total of 912 amyloid‐positive participants were included (198 NC, 504 MCI, and 210 AD). RESULTS Individuals with AD reported more sleep disturbances than NC and MCI participants. Those with sleep disturbances had more WMHs than those without sleep disturbances in the AD group. Mediation analysis revealed an effect of regional WMH burden on the relationship between sleep disturbance and future cognition. DISCUSSION These results suggest that WMH burden and sleep disturbance increase from aging to AD. Sleep disturbance decreases cognition through increases in WMH burden. Improved sleep could mitigate the impact of WMH accumulation and cognitive decline.