The aim of this research is to assess the impact of future climate change on hydrological parameters (e.g., precipitation and temperature) in Ethiopia’s upper Genale River basin. Future climate scenarios for the 2021–2050 and 2051–2080 periods were developed from four different GCM–RCM combinations of CORDEX-Africa projections using the Representative Concentration Pathways (RCP 4.5 and RCP 8.5). These climate models were bias corrected and used as input to the Soil and Water Assessment Tool (SWAT) model. During the 2030s (2021–2050) and 2060s (2051–2080), under the two RCPs, the projected precipitation in the annual and seasonal periods tends to decrease while temperatures increase. The simulated result revealed a significant change in hydrological components (e.g., During the 2060s), under the RCP4.5 scenario, CNRM-CM5 climate model runoff, ground water flow, and total water yield increased by 24.47%, 27.98%, and 28.56%, respectively. On the contrary, during the 2060s under the MIROC5 climate model, runoff, ground water flow, and total water yield reduced by 20.84%, 34.34%, and 25.8%, respectively. The annual hydrological components of the study area under MPI-ESM-LR, EC-EARTH, and MIROC5 showed a decrease in total water yield, surface runoff, ground waterflow, and lateral flow. However, due to a rise in temperature, evapotranspiration showed an increase up to 8.1% under all climate models (MPI-ESM-LR, EC-EARTH, CNRM-CM5, and MIROC5). The reduction in rainfall, which coincides with rising temperatures, is expected to reduce annual water yield, surface runoff, ground waterflow, and lateral flow by up to 39.8%, 39.3%, 50%, and 40.1%, respectively, across MPI-ESM-LR, EC-EARTH, and MIROC5 scenarios for the entire study basin in future projections. Our study helps to give a better insight into understanding climate change in watershed and can benefit the planning of water resources by strengthening adaptation strategies against the impacts of future climate change.