To support implementation of the Paris Agreement, the new HAPPI ensemble of 20 bias-corrected simulations of four climate models was used to drive two global hydrological models, WaterGAP and LPJmL, for assessing freshwater-related hazards and risks in worlds approximately 1.5 °C and 2 °C warmer than pre-industrial. Quasi-stationary HAPPI simulations are better suited than transient CMIP-like simulations for assessing hazards at the two targeted long-term global warming (GW) levels. We analyzed seven hydrological hazard indicators that characterize freshwater-related hazards for humans, freshwater biota and vegetation. Using a strict definition for significant differences, we identified for all but one indicator that areas with either significantly wetter or drier conditions (calculated as percent changes from 2006–2015) are smaller in the 1.5 °C world. For example, 7 day high flow is projected to increase significantly on 11% and 21% of the global land area at 1.5 °C and 2 °C, respectively. However, differences between hydrological hazards at the two GW levels are significant on less than 12% of the area. GW affects a larger area and more people by increases—rather than by decreases—of mean annual and 1-in-10 dry year streamflow, 7 day high flow, and groundwater recharge. The opposite is true for 7 day low flow, maximum snow storage, and soil moisture in the driest month of the growing period. Mean annual streamflow shows the lowest projected percent changes of all indicators. Among country groups, low income countries and lower middle income countries are most affected by decreased low flows and increased high flows, respectively, while high income countries are least affected by such changes. The incremental impact between 1.5 °C and 2 °C on high flows would be felt most by low income and lower middle income countries, the effect on soil moisture and low flows most by high income countries.