The projection of future hydrological processes can provide insights into the risks associated with potential hydrological events in a changing environment and help develop strategies to cope with and prevent them. The Heihe River basin in Northwest China is crucial for providing water resources to water-scarce regions. Thus, understanding the future runoff trends in the context of climate change can optimize water allocation, alleviate water shortages, and mitigate flood risks in the region. In this study, we use meteorological data from 10 general circulation models under two future scenarios to drive the Soil and Water Assessment Tool (SWAT) model and project hydrological processes in the upper Heihe River basin from 2026 to 2100. After examining the future changes in total runoff in the basin, we assess the magnitude, frequency, and timing of daily flood events in the future. The results of the multi-model ensemble averaging (MMEA) method show that the change in the multi-year average annual runoff is −4.5% (2026–2050), −1.8% (2051–2075), and +2.0% (2076–2100) under the SSP245 scenario and −1.0% (2026–2050), +0.4% (2051–2075), and +0.2% (2076–2100) under the SSP585 scenario compared to the historical period. The analysis of flood magnitudes indicates that the basin will experience higher-magnitude floods in the future, with the largest increase rates of 61.9% and 66.4% for the 1-day maximum flows under the SSP245 and SSP585 scenarios, respectively. The flood return period is projected to be shorter in the future, and the 1-day maximum flows of a 100-year flood are expected to increase by 44.7% and 63.7% under the SSP245 and SSP585 scenarios, respectively. Furthermore, a significant shift in the flood timing is expected, with the highest frequency moving from July to August, representing a one-month lag compared to the historical period. Our findings suggest that the hydrological characteristics of the upper Heihe River basin may be significantly altered in the future due to the effects of climate change, resulting in floods with higher magnitudes and frequencies and different timings. Therefore, it is imperative to consider these changes carefully when developing risk prevention measures.