The Cerrado is the largest South American savanna and encompasses substantial species diversity and environmental variation. Nevertheless, little is known regarding the influence of the environment on population divergence of Cerrado species. Here, we searched for climatic drivers of genetic (nuclear microsatellites) and leaf trait divergence in Annona crassiflora, a widespread tree in the Cerrado. The sampling encompassed all phytogeographic provinces of the continuous area of the Cerrado and included 397 individuals belonging to 21 populations. Populations showed substantial genetic and leaf trait divergence across the species' range. Our data revealed three spatially defined genetic groups (eastern, western and southern) and two morphologically distinct groups (eastern and western only). The east-west split in both the morphological and genetic data closely mirrors previously described phylogeographic patterns of Cerrado species. Generalized linear mixed effects models and multiple regression analyses revealed several climatic factors associated with both genetic and leaf trait divergence among populations of A. crassiflora. Isolation by environment (IBE) was mainly due to temperature seasonality and precipitation of the warmest quarter. Populations that experienced lower precipitation summers and hotter winters had heavier leaves and lower specific leaf area. The southwestern area of the Cerrado had the highest genetic diversity of A. crassiflora, suggesting that this region may have been climatically stable. Overall, we demonstrate that a combination of current climate and past climatic changes have shaped the population divergence and spatial structure of A. crassiflora. However, the genetic structure of A. crassiflora reflects the biogeographic history of the species more strongly than leaf traits, which are more related to current climate.