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Accumulation of mutant mitochondrial DNA (mtDNA) heteroplasmy is among the strongest signatures of ageing. Here we investigated the underlying mechanism by calling mtDNA sequence, mtDNA abundance and mtDNA heteroplasmic variants in human blood using whole-genome sequences from approximately 750,000 individuals. We observed that mtDNA single-nucleotide variants (mtSNVs) accumulate sharply at age 60 years, occur at low levels of heteroplasmy, exhibit little evidence of positive selection and are likely to be predominantly neutral. The mutational spectrum of mtSNVs does not reflect oxidative lesions, as is commonly invoked, but is more consistent with mtDNA replication errors. To understand why mtSNVs become detectable with age, we performed a genome-wide association study for heteroplasmic mtSNV burden, identifying germline variants near TERT, TCL1A and SMC4, all of which have been linked to clonal haematopoiesis (CH). Rare-variant analysis also showed that high mtSNV burden is associated with mutations in numerous CH driver genes. These genetic associations persisted even after exclusion of individuals with known CH driver mutations. Our results support a model in which 'cryptic' mtDNA mutations initially arise randomly as replication errors but are undetectable in bulk. They then become apparent only through age-related expansion of cellular clones in blood. We propose that the high copy number and mutation rate of mtDNA make it a sensitive blood-based marker of somatic mosaicism due to CH. Our work mechanistically unifies three prominent signatures of ageing: common germline variants in TERT, CH and observed accrual of mtDNA mutations.