Ancient DNA studies have established that Neolithic European populations were descended from Anatolian migrants(1-8) who received a limited amount of admixture from resident huntergatherers(3-5,9). Many open questions remain, however, about the spatial and temporal dynamics of population interactions and admixture during the Neolithic period. Here we investigate the population dynamics of Neolithization across Europe using a high-resolution genome-wide ancient DNA dataset with a total of 180 samples, of which 130 are newly reported here, from the Neolithic and Chalcolithic periods of Hungary (6000-2900 BC, n = 100), Germany (5500-3000 BC, n = 42) and Spain (5500-2200 BC, n = 38). We find that genetic diversity was shaped predominantly by local processes, with varied sources and proportions of hunter-gatherer ancestry among the three regions and through time. Admixture between groups with different ancestry profiles was pervasive and resulted in observable population transformation across almost all cultural transitions. Our results shed new light on the ways in which gene flow reshaped European populations throughout the Neolithic period and demonstrate the potential of time-series-based sampling and modelling approaches to elucidate multiple dimensions of historical population interactions.