Animals have diversified into a bewildering variety of morphological forms exploiting a complex configuration of trophic niches. Their morphological diversity is widely used as an index of ecosystem function, but the extent to which animal traits predict trophic niches and associated ecological processes is unclear. Here we use the measurements of nine key morphological traits for >99% bird species to show that avian trophic diversity is described by a trait space with four dimensions. The position of species within this space maps with 70-85% accuracy onto major niche axes, including trophic level, dietary resource type and finer-scale variation in foraging behaviour. Phylogenetic analyses reveal that these form-function associations reflect convergence towards predictable trait combinations, indicating that morphological variation is organized into a limited set of dimensions by evolutionary adaptation. Our results establish the minimum dimensionality required for avian functional traits to predict subtle variation in trophic niches and provide a global framework for exploring the origin, function and conservation of bird diversity.