Ecologists have long sought to understand the factors controlling the structure of savanna vegetation. Using data from 2154 sites in savannas across Africa, Australia, and South America, we found that increasing moisture availability drives increases in fire and tree basal area, whereas fire reduces tree basal area. However, among continents, the magnitude of these effects varied substantially, so that a single model cannot adequately represent savanna woody biomass across these regions. Historical and environmental differences drive the regional variation in the functional relationships between woody vegetation, fire, and climate. These same differences will determine the regional responses of vegetation to future climates, with implications for global carbon stocks.