Birds are the most diverse living tetrapod group and are a model of large-scale adaptive radiation. Neontological studies suggest a radiation within the avian crown group, long after the origin of flight. However, deep time patterns of bird evolution remain obscure because only limited fossil data have been considered. We analyse cladogenesis and limb evolution on the entire tree of Mesozoic theropods, documenting the dinosaur–bird transition and immediate origins of powered flight. Mesozoic birds inherited constraints on forelimb evolution from non-flying ancestors, and species diversification rates did not accelerate in the earliest flying taxa. However, Early Cretaceous short-tailed birds exhibit both phenotypic release of the hindlimb and increased diversification rates, unparalleled in magnitude at any other time in the first 155 Myr of theropod evolution. Thus, a Cretaceous adaptive radiation of stem-group birds was enabled by restructuring of the terrestrial locomotor module, which represents a key innovation. Our results suggest two phases of radiation in Avialae: with the Cretaceous diversification overwritten by extinctions of stem-group birds at the Cretaceous–Palaeogene boundary, and subsequent diversification of the crown group. Our findings illustrate the importance of fossil data for understanding the macroevolutionary processes generating modern biodiversity.