The environmental factors limiting species' ranges across broad geographic and taxonomic scales are central to questions regarding the geographic variation in biodiversity and impacts of environmental change. However, our understanding remains relatively limited owing to the small-scale, correlative nature of most previous analyses. In this study, we provide a global test of the environmental determinants of range limits in birds, using both stochastic and environmentally deterministic models of range expansion to simulate spatial patterns in the shape of species' distributions. We show that spatial variation in range shape can be well explained by the action of a few key climatic variables in limiting range expansion. Furthermore, we demonstrate that these patterns cannot be explained by random processes alone. In addition, our study also identifies important differences in the factors constraining range expansion between biogeographic realms and between widespread and rare species. Although temperature was the principal climatic determinant of range shape at a global scale, its effects were driven primarily by widespread species, with the ranges of rare taxa better predicted by gradients in precipitation or topography. These key results were robust with respect to the index used to quantify range shape. Our analysis helps resolve long running debates regarding the role of environmentally deterministic and stochastic processes in structuring biodiversity and extends our understanding of the factors limiting species' ranges and the response of broad scale biodiversity patterns to environmental change.