Dementia in Alzheimer’s disease progresses alongside neurodegeneration, but the specific events that cause neuronal dysfunction and death remain poorly understood. During normal ageing, neurons progressively accumulate somatic mutations at rates similar to those of dividing cells which suggests that genetic factors, environmental exposures or disease states might influence this accumulation. Here we analysed single-cell whole-genome sequencing data from 319 neurons from the prefrontal cortex and hippocampus of individuals with Alzheimer’s disease and neurotypical control individuals. We found that somatic DNA alterations increase in individuals with Alzheimer’s disease, with distinct molecular patterns. Normal neurons accumulate mutations primarily in an age-related pattern (signature A), which closely resembles ‘clock-like’ mutational signatures that have been previously described in healthy and cancerous cells. In neurons affected by Alzheimer’s disease, additional DNA alterations are driven by distinct processes (signature C) that highlight C>A and other specific nucleotide changes. These changes potentially implicate nucleotide oxidation, which we show is increased in Alzheimer’s-disease-affected neurons in situ. Expressed genes exhibit signature-specific damage, and mutations show a transcriptional strand bias, which suggests that transcription-coupled nucleotide excision repair has a role in the generation of mutations. The alterations in Alzheimer’s disease affect coding exons and are predicted to create dysfunctional genetic knockout cells and proteostatic stress. Our results suggest that known pathogenic mechanisms in Alzheimer’s disease may lead to genomic damage to neurons that can progressively impair function. The aberrant accumulation of DNA alterations in neurodegeneration provides insight into the cascade of molecular and cellular events that occurs in the development of Alzheimer’s disease.