Understanding how drought is impacted by both natural and human influences is crucial to the sustainable utilization and protection of water resources. We established a drought severity index (DSI) based on the terrestrial water storage anomaly (TWSA) derived from the GRACE satellite to detect drought characteristics and trends over ten major river basins in China from 2002 to 2017. The influence of natural factors (terrestrial water storage components, precipitation, evapotranspiration, runoff, NDVI, and teleconnection factors (ENSO, PDO, NAO, and AO)) and a human factor (LULC) on drought were investigated and quantified from the perspective of water storage components based on the Theil–Sen trend and Mann–Kendall test method, the perspective of climate change based on cross wavelet transforms, and the perspective of water balance based on Random Forest. The results indicated that (1) almost all humid and arid basins experienced major drought periods during 2002–2006 and 2014–2017, respectively. The southern IRB and central YZRB regions exhibited notable declines in DSI trends, while the majority of the HLRB, IRB, LRB, YRB, HRB, and SWRB experienced significant increases in DSI trends; (2) abnormal groundwater decreases were the main cause of drought triggered by insufficient terrestrial water storage in most basins; (3) ENSO was the strongest teleconnection factor in most humid basins, and NAO, PDO, and AO were the strongest teleconnection factors in the arid basins and PRB. Most significant resonance cycles lasted 12–64 months in 2005–2014; and (4) the influence of an anthropogenic driver (LULC) has become as important as, or more important than, natural factors (runoff and teleconnection factors) on hydrological drought.