This study aims to assess the potential impacts of climate change on hydrometeorological variables and drought characteristics in the Ethiopian Bilate watershed. Climate projections under two Representative Concentration Pathways (RCP4.5 and RCP8.5) were obtained from the Coordinated Regional Downscaling Experiment (CORDEX) Africa for the near future (2021–2050) and far future (2071–2100) periods. The Soil and Water Assessment Tool (SWAT) model was applied to assess changes in watershed hydrology with the CORDEX-Africa data. The Standardized Precipitation Index (SPI), Streamflow Drought Index (SDI), and Reconnaissance Drought Index (RDI) were calculated to identify the characteristics of meteorological, hydrological, and agricultural droughts, respectively. Due to a significant rise in temperature, evapotranspiration will increase by up to 16.8% by the end of the 21st century. Under the RCP8.5 scenario, the annual average rainfall is estimated to decrease by 38.3% in the far future period, inducing a reduction of streamflow of up to 37.5%. Projections in reduced diurnal temperature range might benefit crop growth but suggest elevated heat stress. Probabilities of drought occurrence are expected to be doubled in the far future period, with increased intensities for all three types of droughts. These projected impacts will exacerbate water scarcity and threaten food securities in the study area. The study findings provide forward-looking quantitative information for water management authorities and decision-makers to develop adaptive measures to cope with the changing climate.