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This study investigated the impacts of climate change on the hydrology of the Upper Awash Basin, Ethiopia. A soil and water assessment tool (SWAT) model was calibrated and validated against observed streamflow using SWAT CUP. The Mann–Kendall trend test (MK) was used to assess climate trends. Meteorological drought (SPEI) and hydrological drought (SDI) were also investigated. Based on the ensemble mean of five global climate models (GCMs), projected increases in mean annual maximum temperature over the period 2015–2100 (compared with a 1983–2014 baseline) range from 1.16 to 1.73 °C, while increases in minimum temperature range between 0.79 and 2.53 °C. Increases in mean annual precipitation range from 1.8% at Addis Ababa to 45.5% over the Hombole area. High streamflow (Q5) declines at all stations except Ginchi. Low flows (Q90) also decline with Q90 equaling 0 m3 s−1 (i.e., 100% reduction) at some gauging stations (Akaki and Hombole) for individual GCMs. The SPEI confirmed a significant drought trend in the past, while the frequency and severity of drought will increase in the future. The basin experienced conditions that varied from modest dry periods to a very severe hydrological drought between 1986 and 2005. The projected SDI ranges from modestly dry to modestly wet conditions. Climate change in the basin would enhance seasonal variations in hydrological conditions. Both precipitation and streamflow will decline in the wet seasons and increase in the dry seasons. These changes are likely to have an impact on agricultural activities and other human demands for water resources throughout the basin and will require the implementation of appropriate mitigation measures.