Global cooling has been proposed as a driver of the Great Ordovician Biodiversification Event, the largest radiation of Phanerozoic marine animal Life. Yet, mechanistic understanding of the underlying pathways is lacking and other possible causes are debated. Here we couple a global climate model with a macroecological model to reconstruct global biodiversity patterns during the Ordovician. In our simulations, an inverted latitudinal biodiversity gradient characterizes the late Cambrian and Early Ordovician when climate was much warmer than today. During the Mid-Late Ordovician, climate cooling simultaneously permits the development of a modern latitudinal biodiversity gradient and an increase in global biodiversity. This increase is a consequence of the ecophysiological limitations to marine Life and is robust to uncertainties in both proxy-derived temperature reconstructions and organism physiology. First-order model-data agreement suggests that the most conspicuous rise in biodiversity over Earth’s history – the Great Ordovician Biodiversification Event – was primarily driven by global cooling.