This study assesses future climate change impacts on the hydrologic response of the Upper Meghna River Basin (UMRB), a major river system in Bangladesh. Separate SWAT (Soil and Water Assessment Tool) hydrologic models were developed for the three major sub-basins of the UMRB, i.e., Barak, Meghalaya, and Tripura, considering their unique geographical, hydrological, and land-use characteristics. To evaluate the efficiency of multi-site modeling in providing better model performance, the SWAT models were calibrated at both single and multiple locations. Those models were then simulated to estimate future flows using climate projection data from thirteen CMIP6 General Circulation Models (GCMs) under moderate and extreme emission scenarios, SSP2-4.5, and SSP5-8.5. The results revealed that the annual maximum flow will keep increasing gradually with time. The outlets of the Meghalaya sub-basin will experience a more significant rise in future flow in the upcoming decades compared to the Barak and Tripura sub-basins. Results showed that dry season flows with increases of up to 31–50% would be less affected compared to the wet periods, which could experience increases of up to 47–66%) across the sub-basins by the end of the 21st century under extreme emission projections. Besides an increasing trend in the mean flow, future flows at several outlets also exhibited an escalation in the intensity and frequency of extreme flood events.