The intensity, duration, and geographic extent of floods in Bangladesh mostly depend on the combined influences of three river systems, the Ganges, Brahmaputra and Meghna (GBM). In addition, climate change is likely to have significant effects on the hydrology and water resources of the GBM basin and may ultimately lead to more serious floods in Bangladesh. However, the assessment of climate change impacts on the basin-scale hydrology by using well-calibrated hydrologic modeling has seldom been conducted in the GBM basin due to the lack of observed data for calibration and validation. In this study, a macroscale hydrologic model H08 has been applied over the basin at a relatively fine grid resolution (10 km) by integrating the fine-resolution DEM (digital elevation model) data for accurate river networks delineation. The model has been calibrated via the analysis of model parameter sensitivity and validated based on long-term observed daily streamflow data. The impacts of climate change (considering a high-emissions path) on runoff, evapotranspiration, and soil moisture are assessed by using five CMIP5 (Coupled Model Intercomparison Project Phase 5) GCMs (global circulation models) through three time-slice experiments; the present-day (1979–2003), the near-future (2015–2039), and the far-future (2075–2099) periods. Results show that, by the end of 21st century, (a) the entire GBM basin is projected to be warmed by ~4.3 °C; (b) the changes of mean precipitation (runoff) are projected to be +16.3% (+16.2%), +19.8% (+33.1%), and +29.6% (+39.7%) in the Brahmaputra, Ganges, and Meghna, respectively; and (c) evapotranspiration is projected to increase for the entire GBM (Brahmaputra: +16.4%, Ganges: +13.6%, Meghna: +12.9%) due to increased net radiation as well as warmer temperature. Future changes of hydrologic variables are larger in the dry season (November–April) than in the wet season (May–October). Amongst the three basins, the Meghna shows the highest increase in runoff, indicating higher possibility of flood occurrence. The uncertainty due to the specification of key model parameters in model predictions is found to be low for estimated runoff, evapotranspiration and net radiation. However, the uncertainty in estimated soil moisture is rather large with the coefficient of variation ranging from 14.4 to 31% among the three basins.