As a costliest natural hazard, drought profoundly affects water resources, agriculture, and socio-economic sectors in India. In spite of large spatio-temporal variability in droughts, the propagation time from meteorological to hydrological droughts is not examined at local scale over India. In this study, the meteorological and hydrological variables are obtained at a grid resolution of 0.5 degrees Lat x 0.5 degrees Lon over India to estimate the time of propagation. Here, five different runoff datasets from ERA5, FLDAS, GLDAS, MEERA2, and NCEP are collected. The Standardised Precipitation Evapotranspiration Index (SPEI), and Standardised Runoff Index (SRI) are estimated under the influence of external global and regional drivers. The drought propagation time is computed in 1170 grids blanketing the entire India based on differences between the initiation to initiation (As), peak to peak (Ap) and termination to termination (Ae). In addition, the internal propagation of hydrological drought is estimated with the help of variable motion relationship of speed-time process. The large duration and more severe hydrological droughts are observed mostly over southern and northern parts of India. The drought propagation time varies between 4 and 9 months, 9 to 12 months, and 15 to 20 months in the cases of As, Ap, and Ae, respectively. The drought development and recovery duration are computed as 3.1 to 6 months over most of the areas. It is found that locations with the high value (greater than 10 months) of Drought Development Period (DDP) are also having high value of Drought Recovery Period (DRP). The internal propagation of hydrological drought ranges between the magnitude of 0.4 and 0.6 per month over most of the area in India. It is found that the drought propagation and its characteristics are underestimated over most of the regions in India when computed without the external drivers. The present study would provide important drought characteristics at local scale which can assist water managers and policy makers to devise sustainable management practices.