At least 10,000 virus species have the capacity to infect humans, but at present, the vast majority are circulating silently in wild mammals. However, climate and land use change will produce novel opportunities for viral sharing among previously geographically-isolated species of wildlife3,4. In some cases, this will facilitate zoonotic spillover—a mechanistic link between global environmental change and disease emergence. Here, we simulate potential hotspots of future viral sharing, using a phylogeographic model of the mammal-virus network, and projections of geographic range shifts for 3,139 mammal species under climate change and land use scenarios for the year 2070. We predict that species will aggregate in new combinations at high elevations, in biodiversity hotspots, and in areas of high human population density in Asia and Africa, driving the novel cross-species transmission of their viruses an estimated 4,000 times. Because of their unique dispersal capacity, bats account for the majority of novel viral sharing, and are likely to share viruses along evolutionary pathways that will facilitate future emergence in humans. Surprisingly, we find that this ecological transition may already be underway, and holding warming under 2 °C within the century will not reduce future viral sharing. Our findings highlight an urgent need to pair viral surveillance and discovery efforts with biodiversity surveys tracking species’ range shifts, especially in tropical regions that harbor the most zoonoses and are experiencing rapid warming.