Traditional drought monitoring is based on observed data from both meteorological and hydrological stations. Due to the scarcity of station observation data, it is difficult to obtain accurate drought distribution characteristics, and also tedious to replicate the large-scale information of drought. Thus, Gravity Recovery and Climate Experiment (GRACE) data are utilized in monitoring and characterizing regional droughts where ground station data is limited. In this study, we analyzed and assessed the drought characteristics utilizing the GRACE Groundwater Drought Index (GGDI) over four major river basins in India during the period of 2003–2016. The spatial distribution, temporal evolution of drought, and trend characteristics were analyzed using GGDI. Then, the relationship between GGDI and climate factors were evaluated by the method of wavelet coherence. The results indicate the following points: GRACE’s quantitative results were consistent and robust for drought assessment; out of the four basins, severe drought was noticed in the Cauvery river basin between 2012 and 2015, with severity of −27 and duration of 42 months; other than Godavari river basin, the remaining three basins displayed significant negative trends at monthly and seasonal scales; the wavelet coherence method revealed that climate factors had a substantial effect on GGDI, and the impact of Southern Oscillation Index (SOI) on drought was significantly high, followed by Sea Surface Temperature (SST) Index (namely, NINO3.4) and Multivariate El Niño–Southern Oscillation Index (MEI) in all the basins. This study provides reliable and robust quantitative result of GRACE water storage variations that shares new insights for further drought investigation.