Starting around 50,000 years ago, most large terrestrial animals went extinct in most continents. These extinctions have been attributed either to climatic changes, impacts of human dispersal across the world or a synergy among both. Most studies regarding these extinctions, however, have focused on particular continents or used low-resolution analyses. We used recent advances in fossil dating and past climatic models in a high-resolution quantitative analysis, comparing the explanatory power of the hypotheses at global scale. The timing of human arrival to each region was the best explanation for the extinctions. Climatic effects, where present, were additive rather than synergistic with human arrival. While climatic variation was a contributory cause that helped explaining the process, anthropogenic impacts were the necessary cause that drove it.