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Multidecadal "megadroughts" were a notable feature of the climate of the American Southwest over the Common era, yet we still lack a comprehensive theory for what caused these megadroughts and why they curiously only occurred before about 1600 CE. Here, we use the Paleo Hydrodynamics Data Assimilation product, in conjunction with radiative forcing estimates, to demonstrate that megadroughts in the American Southwest were driven by unusually frequent and cold central tropical Pacific sea surface temperature (SST) excursions in conjunction with anomalously warm Atlantic SSTs and a locally positive radiative forcing. This assessment of past megadroughts provides the first comprehensive theory for the causes of megadroughts and their clustering particularly during the Medieval era. This work also provides the first paleoclimatic support for the prediction that the risk of American Southwest megadroughts will markedly increase with global warming.