The transition from hunting and gathering to farming involved profound cultural and technological changes. In Western and Central Europe, these changes occurred rapidly and synchronously after the arrival of early farmers of Anatolian origin [1-3], who largely replaced the local Mesolithic hunter-gatherers [1, 4-6]. Further east, in the Baltic region, the transition was gradual, with little or no genetic input from incoming farmers [7]. Here we use ancient DNA to investigate the relationship between hunter-gatherers and farmers in the Lower Danube basin, a geographically intermediate area that is characterized by a rapid Neolithic transition but also by the presence of archaeological evidence that points to cultural exchange, and thus possible admixture, between hunter-gatherers and farmers. We recovered four human paleogenomes (1.1× to 4.1× coverage) from Romania spanning a time transect between 8.8 thousand years ago (kya) and 5.4 kya and supplemented them with two Mesolithic genomes (1.7× and 5.3×) from Spain to provide further context on the genetic background of Mesolithic Europe. Our results show major Western hunter-gatherer (WHG) ancestry in a Romanian Eneolithic sample with a minor, but sizeable, contribution from Anatolian farmers, suggesting multiple admixture events between hunter-gatherers and farmers. Dietary stable-isotope analysis of this sample suggests a mixed terrestrial/aquatic diet. Our results provide support for complex interactions among hunter-gatherers and farmers in the Danube basin, demonstrating that in some regions, demic and cultural diffusion were not mutually exclusive, but merely the ends of a continuum for the process of Neolithization.