Terrestrial Water Storage (TWS) over major river basins refers to the total amount of water stored on and beneath the land surface, including surface water, soil moisture, snow, and groundwater. It plays a vital role in regulating the hydrological cycle, sustaining ecosystems, supporting agriculture, human needs, and determining basin yield. The variation in TWS over time is influenced by climatic factors such as precipitation and evapotranspiration, and human activities such as irrigation, dam operations, and groundwater extraction. Therefore, it is necessary to identify the major drivers responsible for the spatiotemporal variation of TWS in the basin. The Indus River Basin is one of South Asia's largest and most significant river basins, spanning over China (Tibet), India, and Pakistan. The Indus River originates on the Tibetan Plateau and flows through India's Ladakh area before entering Pakistan and finally flowing into the Arabian Sea. The basin's topography is diverse, ranging from Himalayan glaciers to dry plains. Major tributaries include the Jhelum, Chenab, Ravi, Beas, and Sutlej, all of which originate in the Himalayas and contribute considerably to the basin's flow. Currently, the basin is experiencing major challenges such as groundwater extraction, water pollution, sedimentation due to rapid urbanisation and irrigation, necessitating robust integrated water management for long-term sustainability. The TWS across large basins is evaluated by simulating various hydrological storage components by using a coupled hydrological-groundwater flow model like SWAT-MODLFOW. The SWAT-MODFLOW model is calibrated and validated by using observed streamflow and groundwater head datasets. The innovative aspect of the present study is addressed by utilising various machine learning (ML) models to enhance the precision of the coupled SWAT-MODFLOW model in estimating TWS. Finally, the simulated TWS is validated by using TWS obtained from the GRACE and GRACE-FO satellite missions, which aids in identifying surplus and deficit regions. This study also demonstrates the factors contributing to fluctuations in terrestrial water storage components, including soil moisture, groundwater, and surface water. Furthermore, this investigation concludes by evaluating which tributary has the most significant potential to contribute surface water and groundwater to a higher-order river and identifying the tributaries impacted by groundwater drought.