Drought is one of the most challenging climatic events. Recently, the drought influence in East Africa (EA) total water storage (TWS) is a serious problem, particularly in arid areas with modified natural vegetation relying on water deficit, garnered extensive research interest. Hydro-climatological and vegetation indices and remote sensing datasets derived from Gravity Recovery Climate Experiment (GRACE) mission datasets reveal good performance in analyzing hydrological drought influences in water storage. Over the last decades, studies were considered successful in monitoring the drought influence in the region TWS potential. However, several challenges remained unsolved, hindering the hydrological drought mitigation strategies. This review deals with an overview of drought impact monitoring targeted at the TWS variation with the response of vegetation change for sustainable drought mitigation. To improve the flexibility and adaptive capacities of the water deficit problem, we aim to provide an overview of drought impacts on TWS in the region to redefine the hydro-climatological and vegetation drought indices and improve the understanding of drought impact through remote sensing datasets. This review presents the challenges and prospects and offers a conclusion. Although, we hope that the review can facilitate further study regarding future hydrological drought projection in the development of several scientific research in the field.