Aging is the leading risk factor for cancer. While it's been proposed that the age-related accumulation of somatic mutations drives this relationship, it is likely not the full story. Here, we show that both aging and cancer share a common epigenetic replication signature, which we modeled from DNA methylation data in extensively passaged immortalized human cells in vitro and tested on clinical tissues. This epigenetic signature of replication, termed CellDRIFT, increased with age across multiple tissues, distinguished tumor from normal tissue, and was escalated in normal breast tissue from cancer patients. Additionally, within-person tissue differences were correlated with both predicted lifetime tissue-specific stem cell divisions and tissue-specific cancer risk. Overall, our findings suggest that age-related replication drives epigenetic changes in cells, pushing them towards a more tumorigenic state.