Tropical forests are some of the most biodiverse ecosystems in the world, yet their functioning is threatened by anthropogenic disturbances and climate change. Global actions to conserve tropical forests could be enhanced by having local knowledge on the forests' functional diversity and functional redundancy as proxies for their capacity to respond to global environmental change. Here we create estimates of plant functional diversity and redundancy across the tropics by combining a dataset of 16 morphological, chemical and photosynthetic plant traits sampled from 2,461 individual trees from 74 sites distributed across four continents together with local climate data for the past half century. Our findings suggest a strong link between climate and functional diversity and redundancy with the three trait groups responding similarly across the tropics and climate gradient. We show that drier tropical forests are overall less functionally diverse than wetter forests and that functional redundancy declines with increasing soil water and vapour pressure deficits. Areas with high functional diversity and high functional redundancy tend to better maintain ecosystem functioning, such as aboveground biomass, after extreme weather events. Our predictions suggest that the lower functional diversity and lower functional redundancy of drier tropical forests, in comparison with wetter forests, may leave them more at risk of shifting towards alternative states in face of further declines in water availability across tropical regions.