The extent to which the transition to agriculture in Europe was the result of biological (demic) diffusion from the Near East or the adoption of farming practices by indigenous hunter-gatherers is subject to continuing debate. Thus far, archaeological study and the analysis of modern and ancient European DNA have yielded inconclusive results regarding these hypotheses. Here we test these ideas using an extensive craniometric dataset representing 30 hunter-gatherer and farming populations. Pairwise population craniometric distance was compared with temporally controlled geographical models representing evolutionary hypotheses of biological and cultural transmission. The results show that, following the physical dispersal of Near Eastern/Anatolian farmers into central Europe, two biological lineages were established with limited gene flow between them. Farming communities spread across Europe, while hunter-gatherer communities located in outlying geographical regions adopted some cultural elements from the farmers. Therefore, the transition to farming in Europe did not involve the complete replacement of indigenous hunter-gatherer populations despite significant gene flow from the Southwest Asia. This study suggests that a mosaic process of dispersal of farmers and their ideas was operating in outlying regions of Europe, thereby reconciling previously conflicting results obtained from genetic and archaeological studies.