The adaptability of species’ climatic niches can influence the dynamics of colonisation and gene flow across climatic gradients, potentially increasing the likelihood of speciation, or reducing extinction in the face of environmental change. However, previous comparative studies have tested these ideas using geographically, taxonomically and ecologically restricted samples, yielding mixed results, and thus the processes linking climatic niche evolution with diversification remain poorly understood. Focusing on birds, the largest and most widespread class of terrestrial vertebrates, we test whether variation in species diversification among clades is correlated with rates of climatic niche evolution, and the extent to which these patterns are modified by underlying gradients in biogeography and species’ ecology. We quantified climatic niches, latitudinal distribution and ecological traits for 7657 (~75%) bird species based on geographical range polygons, and then used Bayesian phylogenetic analyses to test whether niche evolution was related to species richness and rates of diversification across genus and family-level clades. We found that the rate of climatic niche evolution has a positive linear relationship with both species richness and diversification rate at two different taxonomic levels (genus and family). Furthermore, this positive association between labile climatic niches and diversification was detected regardless of variation in clade latitude or key ecological traits. Our findings suggest either that rapid adaptation to unoccupied areas of climatic niche space promotes avian diversification, or that diversification promotes adaptation. Either way, we propose that climatic niche evolution is a fundamental process regulating the link between climate and biodiversity at global scales, irrespective of the geographical and ecological context of speciation and extinction.