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As one of the most destructive and costly natural disasters, drought has far-reaching negative effects on agriculture, water resources, the environment, and human life. Scientific understanding of propagation from meteorological to hydrological drought is of great significance for accurate forecasting of hydrological drought and preventing and mitigating drought disasters. The objective of this study is to analyze the spatio-temporal variational characteristics of propagation from meteorological drought to hydrological drought and the associated driving mechanisms in the eastern Qilian Mountains using the standard precipitation index (SPI), standardized runoff index (SRI), and drought propagation intensity index (DPI). The results show that there has been meteorological humidification and hydrological aridification in the upper reaches of the Shiyang River Basin over the last 56 years; especially in the 2000s, the intensity of hydrological drought was the strongest and the intensity of meteorological drought was the weakest, indicating the propagation intensity of meteorological drought to hydrological drought was extremely strong during this period. The changes of meteorological and hydrological dry–wet are different, both on seasonal and monthly scales. The meteorological dry–wet is shown to have had a significant effect both on the current and month-ahead hydrological dry–wet, where the one-month lag effect was most obvious. The relationship between meteorological and hydrological droughts also vary in space: Hydrological aridification in the Huangyang River, and the rivers east of it, was greater than that in the western tributaries. The drought propagation intensities from west to east showed a decreasing trend, excluding the Huangyang River. Climate and land-use changes are the main factors affecting the propagation from meteorological drought to hydrological drought. When the natural vegetation area accounted for between 76.3–78%, the cultivated land area between 0.55–3.6% and the construction area between 0.08–0.22% were a peer-to-peer propagation process from meteorological drought to hydrological drought in the upper reaches of the Shiyang River.