As modern humans migrated out of Africa, they encountered many new environmental conditions, including greater temperature extremes, different pathogens and higher altitudes. These diverse environments are likely to have acted as agents of natural selection and to have led to local adaptations. One of the most celebrated examples in humans is the adaptation of Tibetans to the hypoxic environment of the high-altitude Tibetan plateau. A hypoxia pathway gene, EPAS1, was previously identified as having the most extreme signature of positive selection in Tibetans, and was shown to be associated with differences in haemoglobin concentration at high altitude. Re-sequencing the region around EPAS1 in 40 Tibetan and 40 Han individuals, we find that this gene has a highly unusual haplotype structure that can only be convincingly explained by introgression of DNA from Denisovan or Denisovan-related individuals into humans. Scanning a larger set of worldwide populations, we find that the selected haplotype is only found in Denisovans and in Tibetans, and at very low frequency among Han Chinese. Furthermore, the length of the haplotype, and the fact that it is not found in any other populations, makes it unlikely that the haplotype sharing between Tibetans and Denisovans was caused by incomplete ancestral lineage sorting rather than introgression. Our findings illustrate that admixture with other hominin species has provided genetic variation that helped humans to adapt to new environments.