Destructive and costly flooding can occur when warm storm systems deposit substantial rain on extensive snowcover, as observed in February 2017 with the Oroville Dam crisis in California. However, decision-makers lack guidance on how such rain-on-snow (ROS) flood risk may respond to climate change. Here, daily ROS events with flood-generating potential are simulated over western North America for a historical (2000–2013) and future (forced under Representative Concentration Pathway 8.5) period with the Weather Research and Forecasting model; 4 km resolution allows the basin-scale ROS flood risk to be assessed. In the warmer climate, we show that ROS becomes less frequent at lower elevations due to snowpack declines, particularly in warmer areas (for example, the Pacific maritime region). By contrast, at higher elevations where seasonal snowcover persists, ROS becomes more frequent due to a shift from snowfall to rain. Accordingly, the water available for runoff increases for 55% of western North American river basins, with corresponding increases in flood risk of 20–200%, the greatest changes of which are projected for the Sierra Nevada, the Colorado River headwaters and the Canadian Rocky Mountains. Thus, flood control and water resource planning must consider ROS to fully quantify changes in flood risk with anthropogenic warming.