Predator-prey interactions play an important role for species composition and community dynamics at local scales, but their importance in shaping large-scale gradients of species richness remains unexplored. Here, we use global range maps, structural equation models (SEM), and comprehensive databases of dietary preferences and body masses of all terrestrial, non-volant mammals worldwide, to test whether (1) prey bottom-up or predator top-down relationships are important drivers of broad-scale species richness gradients once the environment and human influence have been accounted for, (2) predator-prey richness associations vary among biogeographic regions, and (3) body size influences large-scale covariation between predators and prey. SEMs including only productivity, climate, and human factors explained a high proportion of variance in prey richness (R2=0.56) but considerably less in predator richness (R2=0.13). Adding predator-to-prey or prey-to-predator paths strongly increased the explained variance in both cases (prey R2=0.79, predator R2=0.57), suggesting that predator-prey interactions play an important role in driving global diversity gradients. Prey bottom-up effects prevailed over productivity, climate, and human influence to explain predator richness, whereas productivity and climate were more important than predator top-down effects for explaining prey richness, although predator top-down effects were still significant. Global predator-prey associations were not reproduced in all regions, indicating that distinct paleoclimate and evolutionary histories (Africa and Australia) may alter species interactions across trophic levels. Stronger cross-trophic-level associations were recorded within categories of similar body size (e.g., large prey to large predators) than between them (e.g., large prey to small predators), suggesting that mass-related energetic and physiological constraints influence broad-scale richness links, especially for large-bodied mammals. Overall, our results support the idea that trophic interactions can be important drivers of large-scale species richness gradients in combination with environmental effects.