Present-day Tibetans have adapted both genetically and culturally to the high altitude environment of the Tibetan Plateau, but fundamental questions about their origins remain unanswered. Recent archaeological and genetic research suggests the presence of an early population on the Plateau within the past 40 thousand years, followed by the arrival of subsequent groups within the past 10 thousand years. Here, we obtain new genome-wide data for 33 ancient individuals from high elevation sites on the southern fringe of the Tibetan Plateau in Nepal, who we show are most closely related to present-day Tibetans. They derive most of their ancestry from groups related to Late Neolithic populations at the northeastern edge of the Tibetan Plateau but also harbor a minor genetic component from a distinct and deep Paleolithic Eurasian ancestry. In contrast to their Tibetan neighbors, present-day non-Tibetan Tibeto-Burman speakers living at mid-elevations along the southern and eastern margins of the Plateau form a genetic cline that reflects a distinct genetic history. Finally, a comparison between ancient and present-day highlanders confirms ongoing positive selection of high altitude adaptive alleles.