The propagation from meteorological to hydrological drought is critical for better understanding hydrological drought. However, how climate change would affect the drought propagation has not been well studied, especially over regions mixed with massive human interventions. The study attempts to explore changes in the characteristics of meteorological and hydrological droughts, and the corresponding drought propagation under different climate change scenarios across six watersheds over the Yangtze River basin (YZB). Seasonal meteorological and hydrological droughts were characterized by using standardized precipitation and streamflow index at 3‐month scales (SPI‐3 and SSI‐3), which were calculated using precipitation simulations from 15 Coupled Model Intercomparison Project Phase 6 (CMIP6) climate models and streamflow simulations from PCR‐GLOBWB 2.0 hydrological model driven by CMIP6 outputs. Drought propagation characteristics, including propagation ratio, lag and lengthening, were then determined. Both meteorological and hydrological drought durations would shorten, while their drought severity would increase excluding a downstream watershed. About 40%–50% of meteorological droughts could develop into hydrological droughts, with lag time less than 1.4 months and lengthening time less than 1.8 months, respectively. Under climate warming, the drought propagation ratio would increase over two watersheds, while decrease and then increase over three watersheds. The drought propagation lag time is expected to prolong over the regions above Cuntan under moderate emission scenario, while prolong first and then shorten over most watersheds under high‐emission scenario. The drought propagation lengthening time would shorten over most watersheds excluding a downstream watershed, where drought conditions would further worsen during drought propagation. This study calls for climate mitigation efforts to suppress drought aggravation in the propagation particularly for the downstream YZB.