When storm surge and heavy precipitation co-occur, the potential for flooding in low-lying coastal areas is often much greater than from either in isolation. Knowing the probability of these compound events and understanding the processes driving them is essential to mitigate the associated high-impact risks1,2. Here we determine the likelihood of joint occurrence of these two phenomena for the contiguous United States (US) and show that the risk of compound flooding is higher for the Atlantic/Gulf coast relative to the Pacific coast. We also provide evidence that the number of compound events has increased significantly over the past century at many of the major coastal cities. Long-term sea-level rise is the main driver for accelerated flooding along the US coastline3,4; however, under otherwise stationary conditions (no trends in individual records), changes in the joint distributions of storm surge and precipitation associated with climate variability and change also augment flood potential. For New York City (NYC)—as an example—the observed increase in compound events is attributed to a shift towards storm surge weather patterns that also favour high precipitation. Our results demonstrate the importance of assessing compound flooding in a non-stationary framework and its linkages to weather and climate.