A rigorous evaluation of future hydro-climatic changes is necessary for developing climate adaptation strategies for a catchment. The integration of future climate projections from general circulation models (GCMs) in the simulations of a hydrologic model, such as the Soil and Water Assessment Tool (SWAT), is widely considered as one of the most dependable approaches to assess the impacts of climate alteration on hydrology. The main objective of this study was to assess the potential impacts of climate alteration on the hydrology of the Yarra River catchment in Victoria, Australia, using the SWAT model. The climate projections from five GCMs under two Representative Concentration Pathway (RCP) scenarios—RCP 4.5 and 8.5 for 2030 and 2050, respectively—were incorporated into the calibrated SWAT model for the analysis of future hydrologic behaviour against a baseline period of 1990–2008. The SWAT model performed well in its simulation of total streamflow, baseflow, and runoff, with Nash–Sutcliffe efficiency values of more than 0.75 for monthly calibration and validation. Based on the projections from the GCMs, the future rainfall and temperature are expected to decrease and increase, respectively, with the highest changes projected by the GFDL-ESM2M model under the RCP 8.5 scenario in 2050. These changes correspond to significant increases in annual evapotranspiration (8% to 46%) and decreases in other annual water cycle components, especially surface runoff (79% to 93%). Overall, the future climate projections indicate that the study area will become hotter, with less winter–spring (June to November) rainfall and with more water shortages within the catchment.