Gravity Recovery and Climate Experiment (GRACE) and the GRACE-Follow-On (GRACE-FO) gravimetric missions provide essential data for remotely measure large-scale Terrestrial Water Storage (TWS) changes on a regional and global scale. However, during the operating time of the gravimetric missions, monthly or almost yearly data gaps may induce and fail to provide continuous information. Quantifying and predicting the TWS variations is very important for uninterrupted environmental monitoring, to be prepared for the consequences of the climatic change and water resources studies. This paper proposes to predict the TWS variability of 19 global basins from 2019 to 2022 using the traditional Seasonal Autoregressive Integrated Moving Average, Error Trend Seasonal, and Singular Spectrum Analysis as newer time series analysis modeling and prediction approach. For this purpose, the integrated GRACE/GRACE-FO Level-3 Release 06 data from the German Research Centre (GFZ) have been privileged. The accuracy of the resulted TWS predictions has been evaluated based on the use of the mentioned approaches, the cross-validation method, and the root-mean-square-error. Using integrated GRACE/GRACE-FO data, the research strategy in this paper is to become a reference to study the TWS prediction of the new GRACE-FO mission and to bridge the gap between GRACE/GRACE-FO missions. For some global basins, the obtained TWS prediction results reveal a continuous negative or positive TWS during the study period 2019–2022. In conclusion, September 2020 and 2021 are expected to be important dates in terms of TWS decrease affecting all basins in different order of magnitude.