The peopling of the Americas has been the subject of extensive genetic, archaeological and linguistic research; however, central questions remain unresolved. One contentious issue is whether the settlement occurred by means of a single migration or multiple streams of migration from Siberia. The pattern of dispersals within the Americas is also poorly understood. To address these questions at a higher resolution than was previously possible, we assembled data from 52 Native American and 17 Siberian groups genotyped at 364,470 single nucleotide polymorphisms. Here we show that Native Americans descend from at least three streams of Asian gene flow. Most descend entirely from a single ancestral population that we call `First American'. However, speakers of Eskimo-Aleut languages from the Arctic inherit almost half their ancestry from a second stream of Asian gene flow, and the Na-Dene-speaking Chipewyan from Canada inherit roughly one-tenth of their ancestry from a third stream. We show that the initial peopling followed a southward expansion facilitated by the coast, with sequential population splits and little gene flow after divergence, especially in South America. A major exception is in Chibchan speakers on both sides of the Panama isthmus, who have ancestry from both North and South America.