The Amazon Basin is the world’s largest flowing basin and plays an important role in the global hydrological cycle. We combined 20 years of Gravity Recovery and Climate Experiment (GRACE), Swarm, and GRACE Follow-On (GRACE-FO) satellite data to investigate variations of the terrestrial water storage (TWS) from April 2002 to December 2021. We also analyzed the effects of precipitation, surface temperature, and evapotranspiration on TWS changes. Compared with different methods of processing GRACE data, we found that the combined filtering method of P4M6 + Gaussian 300 km in GRACE/GRACE-FO data provided the most accurate results. The long-term trend of TWS was an increase of approximately 0.23 ± 0.11 cm/a in the Amazon Basin, and the central and eastern regions had the highest increase rate, whereas the southeastern region showed a decreasing trend. In the last 20 years, maximum TWS variations occurred in April and minimum TWS variations occurred in October. In spring, the TWS in the Amazon Basin changes considerably from north to south (increasing in the north and decreasing in the south), opposite to that in winter. In the Amazon Basin, precipitation and surface temperature are the important factors affecting the TWS changes, unlike evapotranspiration. In October 2020, the anomalous decreases in TWS changes correlate with insufficient precipitation and rising surface temperatures, which results in a drought.