The indigenous people of the Tibetan Plateau have been the subject of much recent interest because of their unique genetic adaptations to high altitude. Recent studies have demonstrated that the Tibetan EPAS1 haplotype is involved in high altitude-adaptation and originated in an archaic Denisovan-related population. We sequenced the whole-genomes of 27 Tibetans and conducted analyses to infer a detailed history of demography and natural selection of this population. We detected evidence of population structure between the ancestral Han and Tibetan subpopulations as early as 44 to 58 thousand years ago, but with high rates of gene flow until approximately 9 thousand years ago. The CMS test ranked EPAS1 and EGLN1 as the top two positive selection candidates, and in addition identified PTGIS, VDR, and KCTD12 as new candidate genes. The advantageous Tibetan EPAS1 haplotype shared many variants with the Denisovan genome, with an ancient gene tree divergence between the Tibetan and Denisovan haplotypes of about 1 million years ago. With the exception of EPAS1, we observed no evidence of positive selection on Denisovan-like haplotypes.