The definition of drought is very controversial due to its multi-dimensional impact and slow propagation in onset and end. Predicting the accurate occurrence of drought remains a challenging task for researchers. The study focused on hydrological and meteorological drought monitoring and trend analysis in the Abbay river basin, using the streamflow drought index (SDI), standardized precipitation index (SPI), and reconnaissance drought index (RDI), respectively, to fill this research gap. The study also looked into the interrelationships between the two drought indicators. The SDI, SPI, and RDI were calculated using long-term streamflow, precipitation, and temperature data collected from 1973 to 2014. The data were collected from eight streamflow stations and fifteen meteorological gauge stations. DrinC software (Drought Indices Calculator) was used to calculate the SDI, SPI, and RDI values. The result from meteorological drought using SPI12 and RDI12 shows that 1975, 1981, 1984, 1986, 1991, 1994, and 2010 were extreme drought years, whereas 1983, 1984, 2001, and 2010 were the most extreme hydrological drought years based on the SDI12 result. Except for Bahir Dar and Gondar, a severe drought occurs at least once a decade in all stations considered in this study. In general, the SPI, RDI, and SDI results indicated that the study area was exposed to the most prolonged severe and extreme drought from 1981 to 1991. The findings of this study also demonstrated that the occurrence of hydrometeorological droughts in the Abbay river basin has a positive correlation at long time scales of 6 and 12 months. The trend analysis using the Mann–Kendall test implied that there was a significant meteorological drought trend in two stations (Debre Berhan and Fiche) at SPI12 and RDI12 time scale, but for the remaining thirteen stations, there is no trend in all time scales. The hydrological drought trend analysis in the basin on a seasonal (SDI3) and yearly (SDI12) time scale also revealed that three streamflow stations have a positive trend (Kessie, Gummera, and Border). This implies that water resource management is still a vital tool for the sustainable development of the Abbay river basin in the future.