Evapotranspiration is one of the determinant components of the hydrological process, highly influenced by climate change due to the increase in atmospheric temperature at global and regional scales. This study was designed to evaluate the extent to which climate change affects the Potential Evapotranspiration (PET) and the consequent Aridity Index (AI) in the high-emission scenario of Representative Concentration Pathways (RCPs) in the Gilgel Abay, Ribb, Gumara, and Megech watersheds using six Global Climate Models in the 2011–2040, 2041–2070, and 2071–2100 relative to the 1971–2000 (baseline period). The average PET is simulated using the Soil Water Assessment Tool (SWAT) model. Penman-Monteith and Hargreaves methods were used in the computation of PET using the water balance technique, and the Hargreaves method was found more efficient in calibration and validation processes. The Aridity Index (AI) of watersheds is calculated using the ratio of precipitation and potential evapotranspiration. The study revealed that the change in annual average PET is showing an increasing pattern in the three time periods, and the highest rate of changes in Megech, Gilgel Abay, Ribb, and Gumara, watersheds are 16.66%, 15.53%, 14.68%, and 13.46%, respectively in the 2071–2100 time period. Seasonally, the highest rate of change in PET is 20.37% (September), 19.29% (April), 17.46% (March), and 17.02% (March) in the Megech, Gilgel Abay, Ribb, and Gumara, respectively. Similarly, the seasonal highest change in Aridity Index (AI) is also likely to be observed in the 2071–2100 in which in the dry season, it accounts –0.303 (March), –0.299 (March), –0.285 (April), and –0.276 (April) in the Ribb, Gumara, Gilgel Abay, and Megech, respectively, whereas in the rainy season, the change is 0.263, 0.258, 0.238, and 0.211 in the Gilgel Abay, Gumara, Ribb, and Megech, respectively. In general, due to the rising atmospheric temperature, the amount of moisture during dry seasons in the headwater catchments of the upper Blue Nile basin is expected to deplete in the 21st century. Therefore, it is highly recommended to use different climate change adaptation mechanisms including adopting suitable physical and biological water conservation techniques to enhance the amount of water stored in the subsurface and joining the groundwater during the rainy season.