Gravity Recovery and Climate Experiment (GRACE) observations provide information on Total Water Storage Anomaly (TWSA) which is a key variable for drought monitoring and assessment. The so-called Total Water Storage Deficit Index (TWSDI) based on GRACE data has been widely used for characterizing drought events. Here we show that the commonly used TWSDI approach often exhibits significant inconsistencies with meteorological conditions, primarily upon presence of a trend in observations due to anthropogenic water use. In this study, we propose a modified version of TWSDI (termed, MTWSDI) that decomposes the anthropogenic and climatic-driven components of GRACE observations. We applied our approach for drought monitoring over the Ganges-Brahmaputra in India and Markazi basins in Iran. Results show that the newly developed MTWSDI exhibits consistency with meteorological drought indices in both basins. We also propose a deficit-based method for drought monitoring and recovery assessment using GRACE observations, providing useful information about volume of deficit, and minimum and average time for drought recovery. According to the deficit thresholds, water deficits caused by anthropogenic impacts every year in the Ganges-Brahmaputra basin and Markazi basins is almost equal to an abnormally dry condition and a moderate drought condition, receptively. It indicates that unsustainable human water use have led to a form of perpetual and accelerated anthropogenic drought in these basins. Continuation of this trend would deplete the basin and cause significant socio-economic challenges.