A drought-induced water storage deficit index (D-WSDI) is proposed to quantify the response of GRACE-based terrestrial water storage change to meteorological drought and the impact of drought on water storage deficit. D-WSDI is defined as the normalized residual component of GRACE time-series data after removing the long-term trend and seasonal components. The evaluation based on the Emergency Events Database (EM-DAT) showed that more than 90% of global drought events from 2002 to 2019 led to a water storage deficit, which can be detected by the proposed D-WSDI. The severity of the water storage deficit caused by drought increases with the extending drought duration. An average of 73% of water storage deficit months at the global scale is related to precipitation shortages. The cumulative precipitation deficit in relatively short periods of less than 9 months can lead to the water storage deficit in low-latitude regions, whereas a longer time scale is required to lead to a water storage deficit in high-latitude regions. The negative monthly precipitation anomaly of about -20% can lead to a water storage deficit in high rainfall regions, whereas the negative precipitation anomaly can reach -80% in arid and semiarid areas. D-WSDI holds the capability to quantify the water storage deficit caused by drought, especially in the regions with terrestrial water storage change influenced by the long-term trends in climate and anthropogenic activities, and can be used as an index of drought monitoring with similar or superior performance compared to some traditional drought indices.