1. The stress-gradient hypothesis (SGH) predicts an increasing importance of facilitative mechanisms relative to competition along gradients of increasing environmental stress. Although developed across a variety of ecosystems, the SGH's relevance to the dynamic tree—grass systems of global savannas remains unclear. Here, we present a meta-analysis of empirical studies to explore emergent patterns of tree—grass relationships in global savannas in the context of the SGH. 2. We quantified the net effect of trees on understorey grass production relative to production away from tree canopies along a rainfall gradient in tropical and temperate savannas and compared these findings to the predictions of the SGH. We also analysed soil and plant nutrient concentrations in subcanopy and open-grassland areas to investigate the potential role of nutrients in determining grass production in the presence and absence of trees. 3. Our meta-analysis revealed a shift from net competitive to net facilitative effects of trees on subcanopy grass production with decreasing annual precipitation, consistent with the SGH. We also found a significant difference between sites from Africa and North America, suggesting differences in tree—grass interactions in the savannas of tropical and temperate regions. 4. Nutrient analyses indicate no change in nutrient ratios along the rainfall gradient, but consistent nutrient enrichment under tree canopies. 5. Synthesis. Our results help to resolve questions about the SGH in semi-arid systems, demonstrating that in mixed tree—grass systems, trees facilitate grass growth in drier regions and suppress grass growth in wetter regions. Relationships differ, however, between African and North American sites representing tropical and temperate bioclimates, respectively. The results of this meta-analysis advance our understanding of tree—grass interactions in savannas and contribute a valuable data set to the developing theory behind the SGH.