Climate change is primarily responsible for spatiotemporal variability and change in the hydrological processes, particularly in the streamflow of a given area. The objective of this study is to evaluate the hydrological impact of climate change on the Ribb River watershed in the Lake Tana sub-basin, Ethiopia, using the hydrological model SWAT and the Regional Climate Model (RCA4). Climate variables were projected using the CORDEX RCM (RCA4) with a ~50 km spatial resolution under two representative concentration pathway (RCP4.5 and RCP8.5) scenarios for the reference period (1979–2011) and future (2011–2099) climate conditions. A linear-scaling approach was employed for bias correction, and Mann–Kendall trend analysis was used to assess projected climate variable trends. Results indicate an increase in monthly mean temperatures (maximum and minimum) for both RCP scenarios in the future, while precipitation shows no systematic trend. Seasonal analysis reveals increasing precipitation trends in long rainy (JJAS) and dry (ONDJ) seasons but a decrease in short rainy (FMAM) seasons. The SWAT model, calibrated and validated using discharge data from the Ribb River near Addis Zemen (1979–2012), performed well with NSE and R2 values of 0.74 and 0.7, respectively. Future streamflow projections show an increasing trend associated with increased precipitation, varying by 58–66% in dry seasons and 21–55% in wet seasons compared to the reference period, depending on the RCP scenario. These findings suggest that climate change may positively impact the watershed's hydrology, potentially increasing future water availability in the region.