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Meteorological to hydrological drought propagation has been widely studied to reflect the relationship between these drought categories and better understand drought mechanisms. However, global warming may alter the drought propagation features, which are not fully understood. This study aims to investigate changes in meteorological and hydrological drought conditions, especially their propagation features in 1.5–3.0°C warmer climates for 8,655 watersheds globally. First, the three‐month scale standardized precipitation index and the standardized runoff index are calculated based on the precipitation simulated by the 15 global climate models and the runoff simulated by the four hydrological models, respectively. Drought events are then identified using the run theory, followed by the calculation of drought propagation features (i.e., pooling, lag, and lengthening) for matched meteorological and hydrological droughts. As a result, both meteorological and hydrological drought conditions (i.e., duration and severity) would relieve in warmer climates due to increased precipitation for regions excluding Western North America, South America, the Mediterranean, Southern Africa, East Asia, and Australia. However, the drought conditions would be more severe during drought propagation from meteorological to hydrological droughts over most regions. During drought propagation, the worsening drought conditions over half of the regions would be more serious first and then relieved with the rising temperature. These results indicate that efforts to slow down global warming can suppress the deterioration of drought conditions in the propagation. Plain Language Summary: Droughts can be categorized into meteorological, hydrological, agricultural, and socioeconomic types from different impacted aspects. Investigating meteorological to hydrological drought propagation can reflect the relationship between these two drought categories to understand the drought mechanism better. However, it is not fully understood whether global warming would alter the drought propagation features or not. Therefore, we evaluated the change of meteorological and hydrological drought conditions, especially their propagation features in 1.5 to 3.0°C warmer climates for 8,655 watersheds around the world. Here we show that both meteorological and hydrological drought conditions would relieve in warmer climates due to the increase of precipitation for regions excluding Western North America, South America, the Mediterranean, Southern Africa, East Asia, and Australia. However, the drought conditions would be more severe during drought propagation over most regions in warmer climates. Our findings promote a better understanding of drought propagation changes under global warming. Key Points: Both meteorological and hydrological drought conditions are projected to relieve in warmer climates for around half of global regionsThe duration and severity developing from meteorological to hydrological droughts would be more severe over most regionsThe worsening duration and severity during the propagation over half of the regions would intensify first and then ease in warmer climates [ABSTRACT FROM AUTHOR]