Flood event set generation, as employed in catastrophe risk models, relies on gauge information that is not available in data-scarce regions. To overcome this limitation, we develop a stochastic fluvial and pluvial flood model of Southeast Asia, using freely and globally available discharge data from the global hydrological model GloFAS and rainfall from the ERA5 reanalysis. We use a conditional multivariate statistical model to produce a synthetic catalog of 10,000 years of flood events. We calculate the flood population exposure associated with each flood event using freely available population data from WorldPop and generate exposure probability exceedance curves. We validate the population exposure curves against observed flood disaster data from EM-DAT, showing that our methodology provides exposure estimates that are in line with historical observations. We find that there is a 1% probability that more than 30 million people will be exposed to flooding in a given year according to our event set. This number is roughly half the population living in the 100-year return period flood zone of Fathom's hazard maps, suggesting most studies based on static flood maps overestimate exposure. This analysis provides significant progress over previous non-stochastic studies which are only able to compute total or average exposure within a given floodplain area and demonstrates that a reanalysis-based stochastic flood model can be designed to generate reliable estimates of population exposure probability exceedance. This study is a step toward a fully global catastrophe model for floods capable of providing exposure and loss estimates worldwide.