When, where, and how often hominin interbreeding happened is largely unknown. We study the potential for Neanderthal-Denisovan admixture using species distribution models that integrate extensive fossil, archaeological, and genetic data with transient coupled general circulation model simulations of global climate and biomes. Our Pleistocene hindcast of past hominins' habitat suitability reveals pronounced climate-driven zonal shifts in the main overlap region of Denisovans and Neanderthals in central Eurasia. These shifts, which influenced the timing and intensity of potential interbreeding events, can be attributed to the response of climate and vegetation to past variations in atmospheric carbon dioxide and Northern Hemisphere ice-sheet volume. Therefore, glacial-interglacial climate swings likely played an important role in favoring gene flow between archaic humans.