Freshwater stored on land is an extremely vital resource for all the terrestrial life on Earth. But our ability to record the change of land water storage is weak despite its importance. In this study, we attempt to establish a data‐driven model for simulating terrestrial water storage dynamics by relating climate forcings with terrestrial water storage anomalies (TWSAs) from the Gravity Recovery and Climate Experiment (GRACE) satellites. In the case study in Pearl River basin, China, the relationships were learned by using two ensemble learning algorithms, the Random Forest (RF) and eXtreme Gradient Boost (XGB), respectively. The TWSA in the basin was reconstructed back to past decades and compared with the TWSA derived from global land surface models. As a result, the RF and XGB algorithms both perform well and could nicely reproduce the spatial pattern and value range of GRACE observations, outperforming the land surface models. Temporal behaviors of the reconstructed TWSA time series well capture those of both GRACE and land surface models time series. A multiscale GRACE‐based drought index was proposed, and the index matches the Standardized Precipitation‐Evapotranspiration Index time series at different time scales. The case analysis for years of 1963 and 1998 indicates the ability of the reconstructed TWSA for identifying past drought and flood extremes. The importance of different input variables to the TWSA estimation model was quantified, and the precipitation of the prior 2 months is the most important variable for simulating the TWSA of the current month in the model. Results of this study highlight the great potentials for estimating terrestrial water storage dynamics from climate forcing data by using machine learning to achieve comparable results than complex physical models.