Farming was established in Central Europe by the Linearbandkeramik culture (LBK), a well-investigated archaeological horizon, which emerged in the Carpathian Basin, in today's Hungary. However, the genetic background of the LBK genesis has not been revealed yet. Here we present 9 Y chromosomal and 84 mitochondrial DNA profiles from Mesolithic, Neolithic Starčevo and LBK sites (7th/6th millennium BC) from the Carpathian Basin and south-eastern Europe. We detect genetic continuity of both maternal and paternal elements during the initial spread of agriculture, and confirm the substantial genetic impact of early farming south-eastern European and Carpathian Basin cultures on Central European populations of the 6th-4th millennium BC. Our comprehensive Y chromosomal and mitochondrial DNA population genetic analyses demonstrate a clear affinity of the early farmers to the modern Near East and Caucasus, tracing the expansion from that region through south-eastern Europe and the Carpathian Basin into Central Europe. Our results also reveal contrasting patterns for male and female genetic diversity in the European Neolithic, suggesting patrilineal descent system and patrilocal residential rules among the early farmers.