Drought reduces plant productivity, induces widespread plant mortality and limits the geographic distribution of plant species1, 2, 3, 4, 5, 6, 7. As climates warm and precipitation patterns shift in the future8, 9, understanding the distribution of the diversity of plant drought tolerance is central to predicting future ecosystem function and resilience to climate change10, 11, 12. These questions are especially pressing for the world’s 11,000 grass species13, which dominate a large fraction of the terrestrial biosphere14, yet are poorly characterized with respect to responses to drought. Here, we show that physiological drought tolerance, which varied tenfold among 426 grass species, is well distributed both climatically and phylogenetically, suggesting most native grasslands are likely to contain a high diversity of drought tolerance. Consequently, local species may help maintain ecosystem functioning in response to changing drought regimes without requiring long-distance migrations of grass species. Furthermore, physiologically drought-tolerant species had higher rates of water and carbon dioxide exchange than intolerant species, indicating that severe droughts may generate legacies for ecosystem functioning. In all, our findings suggest that diverse grasslands throughout the globe have the potential to be resilient to drought in the face of climate change through the local expansion of drought-tolerant species.