Radiocarbon dating is the gold standard in archeology to estimate the age of skeletons, a key to studying their origins. Many published ancient genomes lack reliable and direct dates, which results in obscure and contradictory reports. Here, we developed the Temporal Population Structure (TPS), the first DNA-based dating method for ancient genomes ranging from the Late Mesolithic to modern-days, and applied it to 3,591 ancient and 1,307 modern Eurasians. We show that TPS predictions align with their known dates and correctly account for kin relationships. TPS dating of poorly dated Eurasian samples resolved conflicting reports in the literature, as illustrated by one test case. We demonstrated how TPS improved the ability to study phenotypic traits over time.