The Gravity Recovery and Climate Experiment (GRACE) satellite data retrieval experiment has been instrumental in characterizing the global fluctuations in terrestrial water storage (ΔTWS) over the past 20 years. Given the limited availability of hydrological data, GRACE measurements are frequently combined with other climatic models, standardized precipitation index (SPI), and standardized temperature index (STI) data to examine the likelihood of such impacts on hydrology and calculate the groundwater storage changes (ΔGWS). The characterization of the intensity and variability of drought events has been identified based on the Terrestrial Water Storage Deficit Index (TWSI), derived from GRACE mass concentration blocks (mascons) over Senegal during the studied period (April 2002–December 2021). The results are: (1) The average annual precipitation (AAP) rate for the entire period was calculated at 692.5 mm/yr. (2) The GRACE-derived ΔTWS variations were calculated at +0.89 ± 0.34, +0.07 ± 0.36, +1.66 ± 1.20, and +0.63 ± 0.08 cm/yr for Periods I (April 2002–December 2009), II (January 2010–December 2017), III (January 2018–December 2021), and the entire period (April 2002–December 2021), respectively. (3) The ΔGWS changes were estimated to be +0.89 ± 0.31, +0.085 ± 0.33, +1.64 ± 1.11, and +0.63 ± 0.08 cm/yr for Periods I, II, II, and the entire period, respectively. (4) There is good agreement in some years and seasons according to the investigation of the link between the GRACE dataset, STI, and SPI. (5) Senegal’s groundwater storage is increasing at a rate of 0.63 ± 0.08 cm/yr (1.24 ± 0.16 km³/yr) between April 2002 and December 2021. (6) Considering the yearly extraction rates of 1.13 ± 0.11 cm/yr (2.22 ± 0.22 km³/yr), an average recharge rate of +1.76 ± 0.14 cm/yr (+3.46 ± 0.28 km³/yr) was calculated for the studied area. The integrated strategy is instructive and economical.