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When different flooding drivers co‐occur, they can cause compound floods. Despite the potential impact of compound flooding, few studies have projected how the joint probability of flooding drivers may change. Furthermore, existing projections may not be very robust, as they are based on only 5 to 6 climate model simulations. Here, we use a large ensemble of simulations from the Coupled Model Intercomparison Project 6 (CMIP6) to project changes in the joint probability of extreme storm surges and precipitation at European tide gauges under a medium and high emissions scenario, enabled by data‐proximate cloud computing and statistical storm surge modeling. We find that the joint probability will increase in the northwest and decrease in most of the southwest of Europe. Averaged over Europe, the absolute magnitude of these changes is 36%–49% by 2080, depending on the scenario. The large‐scale changes in the joint probability of extreme storm surges and precipitation are similar to those in the joint probability of extreme wind speeds and precipitation, but locally, differences can exceed the changes themselves. Due to internal climate variability and inter‐model differences, projections based on simulations of only 5 to 6 randomly chosen CMIP6 models have a probability of higher than 10% to differ qualitatively from projections based on all CMIP6 simulations in multiple regions, especially under the medium emissions scenario and earlier in the twenty‐first century. Therefore, our results provide a more robust and less uncertain representation of changes in the potential for compound flooding in Europe than previous projections. Plain Language Summary: Extreme storm surges, rainfall or river discharge can cause flooding. When these events happen at the same time, even more severe flooding may follow. Climate change could affect the odds that drivers of flooding coincide, potentially leading to larger flood risk. However, few scientists have tried to compute such changes, using only a few different computer models of our climate. Here, we use a much larger set of climate models to compute how the odds that an extreme storm surge coincides with extreme precipitation could change in the future. We find that at the coasts of northwestern Europe, those odds will increase, whereas in southwestern Europe, they will mostly decrease. On average, the changes will be as large as 36%–49% of the current odds, depending on whether the concentration of greenhouse gases in the atmosphere will increase by a medium or a large amount. When we use smaller sets of climate models for our calculations, we get substantially different results in some cases. In conclusion, by using a larger set of climate models than previous studies, we have made more robust computations of how the odds that extreme storm surges and precipitation coincide will change in Europe. Key Points: We project changes in the joint probability of storm surge and precipitation extremes based on a large ensemble of model simulations from the Coupled Model Intercomparison Project 6The joint probability will increase in the northwest and decrease in the southwest of Europe, with an average absolute magnitude of 36%–49%Especially under lower emissions, often more than 5 or 6 climate model simulations are needed to draw robust conclusions on these changes [ABSTRACT FROM AUTHOR]