Climate change is predicted to drive geographical range shifts in many taxa, leading to the formation of novel species assemblages and fluctuations in species richness worldwide. However, the effect of these changes on functional diversity is not yet fully understood, in part because comprehensive species-level trait data are generally lacking at global scales. Here we use morphometric and ecological trait data for 8269 terrestrial bird species to compare functional diversity (FD) of current and future bird assemblages under a medium emissions scenario. We show that future assemblages are likely to undergo substantial shifts in trait structure, with the direction and magnitude of these shifts varying with geographical location and trophic guild. Specifically, invertivore FD is projected to increase at higher latitudes with concurrent losses at mid-latitudes, reflecting poleward shifts in range, whereas frugivore FD is projected to fluctuate in many tropical regions with major declines in much of South America and New Guinea. We show that these projected changes in FD are generally greater than expected from changing species richness alone, indicating that projected FD changes are primarily driven by the loss or gain of functionally distinct species. Our findings suggest that climate change will drive continental-scale shifts in avian functional diversity, with potentially far-reaching implications for ecosystem functions and resilience.