Tropical forest canopies are the biosphere’s most concentrated atmospheric interface for carbon, water and energy^1,2. However, in most Earth System Models, the diverse and heterogeneous tropical forest biome is represented as a largely uniform ecosystem with either a singular or a small number of fixed canopy ecophysiological properties³. This situation arises, in part, from a lack of understanding about how and why the functional properties of tropical forest canopies vary geographically⁴. Here, by combining field-collected data from more than 1,800 vegetation plots and tree traits with satellite remote-sensing, terrain, climate and soil data, we predict variation across 13 morphological, structural and chemical functional traits of trees, and use this to compute and map the functional diversity of tropical forests. Our findings reveal that the tropical Americas, Africa and Asia tend to occupy different portions of the total functional trait space available across tropical forests. Tropical American forests are predicted to have 40% greater functional richness than tropical African and Asian forests. Meanwhile, African forests have the highest functional divergence—32% and 7% higher than that of tropical American and Asian forests, respectively. An uncertainty analysis highlights priority regions for further data collection, which would refine and improve these maps. Our predictions represent a ground-based and remotely enabled global analysis of how and why the functional traits of tropical forest canopies vary across space.