Global cooling during the Ordovician (485 Ma to 443 Ma) has long been considered as a possible driver of the Great Ordovician Biodiversification Event (GOBE), the largest radiation of Phanerozoic marine animal Life. Yet, this hypothesis exclusively relies on temporal correlations. Mechanistic understanding of the underlying pathways is lacking and other possible causes are debated. Here we couple an ocean-atmosphere general circulation model with a macroecological model to reconstruct global biodiversity patterns from 490 Ma to 430 Ma. Our results demonstrate that the GOBE permitted the development of a Modern-like Latitudinal Biodiversity Gradient (LBG). Inverted LBGs, with biodiversity increasing from the equator to the poles, characterize the late Cambrian and Early Ordovician when climate was much warmer than today. A Modern LBG develops in the Mid-Late Ordovician in response to the drop in ocean temperatures. Globally, simulated biodiversity increases due to long-term cooling during the Ordovician. 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 –GOBE– was primarily driven by global cooling.