The Coelurosauria are a group of mostly feathered theropods that gave rise to birds, the only dinosaurians that survived the Cretaceous-Paleogene extinction event and are still found today. Between their first appearance in the Middle Jurassic up to the end Cretaceous, coelurosaurians were party to dramatic geographic changes on the Earth’s surface, including the breakup of the supercontinent Pangaea, and the formation of the Atlantic Ocean. These plate tectonic events are thought to have caused vicariance or dispersal of coelurosaurian faunas, influencing their evolution. Unfortunately, few coelurosaurian biogeographic hypotheses have been supported by quantitative evidence. Here, we report the first, broadly sampled quantitative analysis of coelurosaurian biogeography using the likelihood-based package BioGeoBEARS. Mesozoic geographic configurations and changes are reconstructed and employed as constraints in this analysis, including their associated uncertainties. We use a comprehensive time-calibrated coelurosaurian evolutionary tree produced from the Theropod Working Group phylogenetic data matrix. Six biogeographic models in the BioGeoBEARS package with different assumptions about the evolution of spatial distributions are tested against geographic constraints. Our results statistically favor the DIVALIKE+J and DEC+J models, which allow vicariance and founder events, supporting continental vicariance as an important factor in coelurosaurian evolution. Ancestral range estimation indicates frequent dispersal events via the Apulian route (connecting Europe and Africa during the Early Cretaceous) and the Bering land bridge (connecting North America and Asia during the Late Cretaceous). These quantitative results are consistent with commonly inferred Mesozoic dinosaurian dispersals and continental-fragmentation-induced vicariance events. In addition, we recognize the importance of Europe as a dispersal center and gateway in the Early Cretaceous, as well as other vicariance events such as those triggered by the disappearance of land bridges.