Drought propagation through the terrestrial hydrological cycle is associated with a change in drought characteristics (duration and deficit), moving from precipitation via soil moisture to discharge. Here we investigate climate controls on drought propagation with a modeling experiment in 1271 virtual catchments that differ only in climate type. For these virtual catchments we studied the bivariate distribution of drought duration and standardized deficit for the variables precipitation, soil moisture, and discharge. We found that for meteorological drought (below-normal precipitation), the bivariate distributions of drought characteristics have a linear shape in all climates and are thus not affected by seasonality in climate. Despite the linear shape of meteorological drought, soil moisture drought (below-normal storage in the unsaturated zone) and hydrological drought (below-normal water availability in aquifers, lakes, and/or streams) show strongly nonlinear shapes in drought characteristics in climates with a pronounced seasonal cycle in precipitation and/or temperature. These seasonality effects on drought propagation are found in monsoonal, savannah, and Mediterranean climate zones. In these regions, both soil moisture and discharge show deviating shapes in drought characteristics. The effect of seasonality on drought propagation is even stronger in cold seasonal climates (i.e., at high latitudes and altitudes), where snow accumulation during winter prevents recovery from summer hydrological drought, and deficit increases strongly with duration. This has important implications for water resources management in seasonal climates, which cannot solely rely on meteorology-based indices as proxies for hydrological drought duration and deficit and need to include seasonal variation in both precipitation and temperature in hydrological drought forecasting.