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We investigate the interannual and interdecadal hydrological changes in the Amazon River basin and its sub-basins during the 1980-2015 period using GRACE satellite data and a physically based, 2 km grid continental-scale hydrological model (LEAF-Hydro-Flood) that includes a prognostic groundwater scheme and accounts for the effects of land use-land cover (LULC) change. The analyses focus on the dominant mechanisms that modulate terrestrial water storage (TWS) variations and droughts. We find that (1) the model simulates the basin-averaged TWS variations remarkably well; however, disagreements are observed in spatial patterns of temporal trends, especially for the post-2008 period. (2) The 2010s is the driest period since 1980, characterized by a major shift in the decadal mean compared to the 2000s caused by increased drought frequency. (3) Long-term trends in TWS suggest that the Amazon overall is getting wetter (1.13 mm yr(-1)), but its southern and southeastern subbasins are undergoing significant negative TWS changes, caused primarily by intensified LULC changes. (4) Increasing divergence between dry-season total water deficit and TWS release suggests a strengthening dry season, especially in the southern and southeastern sub-basins. (5) The subsurface storage regulates the propagation of meteorological droughts into hydrological droughts by strongly modulating TWS release with respect to its storage preceding the drought condition. Our simulations provide crucial insight into the importance of sub-surface storage in alleviating surface water deficit across Amazon and open pathways for improving prediction and mitigation of extreme droughts under changing climate and increasing hydrologic alterations due to human activities (e.g., LULC change).