Streamflow prediction is a crucial aspect of water resource management and environmental control. Projected changes in climate variables from Global Climate Models (GCMs) coupled with Global Hydrological Models (GHMs) can be used to study water regimes during baseline and future hydrological conditions in river basins. Multi-model ensemble averaging methods have been widely used to combine the predictions of multiple GCMs-GHMs to produce more accurate and reliable average estimates. This study employs the Bayesian Model Averaging (BMA) technique to simulate values of monthly discharge from five GHMs coupled with projections from five GCMs from the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP—fast track version) during a retrospective period. The BMA technique effectively selects the best-performing GCM-GHM model combinations, and additionally provides a solid framework for uncertainty analysis of ensemble-averaged predictions concerning observed monthly discharge data obtained from the Polavaram region close to the outlet of the Godavari basin from 1971 to 2000. The results show that BMA significantly outperforms traditional averaging approaches like simple model averaging and weighted averaging in predicting streamflow values. The BMA model effectively captures the seasonal fluctuations in the flow data, displaying minor differences in peak flow values while occasionally overestimating the low points in streamflow. This study during the baseline period suggests that BMA is a promising tool for improving the accuracy and reliability of streamflow projections provided by GCM-driven GHMs.