Mobility is one of the most important processes shaping spatiotemporal patterns of variation in genetic, morphological, and cultural traits. However, current approaches for inferring past migration episodes in the fields of archaeology and population genetics lack either temporal resolution or formal quantification of the underlying mobility, are poorly suited to spatially and temporally sparsely sampled data, and permit only limited systematic comparison between different time periods or geographic regions. Here we present an estimator of past mobility that addresses these issues by explicitly linking trait differentiation in space and time. We demonstrate the efficacy of this estimator using spatiotemporally explicit simulations and apply it to a large set of ancient genomic data from Western Eurasia. We identify a sequence of changes in human mobility from the Late Pleistocene to the Iron Age. We find that mobility among European Holocene farmers was significantly higher than among European hunter-gatherers both pre- and postdating the Last Glacial Maximum. We also infer that this Holocene rise in mobility occurred in at least three distinct stages: the first centering on the well-known population expansion at the beginning of the Neolithic, and the second and third centering on the beginning of the Bronze Age and the late Iron Age, respectively. These findings suggest a strong link between technological change and human mobility in Holocene Western Eurasia and demonstrate the utility of this framework for exploring changes in mobility through space and time.