We sequenced the genomes of a [sim]7,000-year-old farmer from Germany and eight [sim]8,000-year-old hunter-gatherers from Luxembourg and Sweden. We analysed these and other ancient genomes with 2,345 contemporary humans to show that most present-day Europeans derive from at least three highly differentiated populations: west European hunter-gatherers, who contributed ancestry to all Europeans but not to Near Easterners; ancient north Eurasians related to Upper Palaeolithic Siberians, who contributed to both Europeans and Near Easterners; and early European farmers, who were mainly of Near Eastern origin but also harboured west European hunter-gatherer related ancestry. We model these populations/’ deep relationships and show that early European farmers had [sim]44% ancestry from a /`basal Eurasian/’ population that split before the diversification of other non-African lineages.