Climate-induced changes in precipitation and temperature can have a profound impact on watershed hydrological regimes, ultimately affecting agricultural yields and the quantity and quality of surface water systems. In India, the majority of the watersheds are facing water quality and quantity issues due to changes in the precipitation and temperature, which requires assessment and adaptive measures. This study seeks to evaluate the effects of climate change on the water quality and quantity at a regional scale in the Nagavali and Vamsadhara watersheds of eastern India. The impact rainfall variations in the study watersheds were modeled using the Soil and Water Assessment Tool (SWAT) with bias-corrected, statistically downscaled models from Coupled Model Intercomparison Project-6 (CMIP-6) data for historical (1975–2014), near future (2022–2060), and far future (2061–2100) timeframes using three Shared Socioeconomic Pathways (SSP) scenarios. The range of projected changes in percentage of mean annual precipitation and mean temperature varies from 0 to 41.7% and 0.7 °C to 2.7 °C in the future climate, which indicates a warmer and wetter climate in the Nagavali and Vamsadhara watersheds. Under SSP245, the average monthly changes in precipitation range from a decrease of 4.6% to an increase of 25.5%, while the corresponding changes in streamflow and sediment yield range from −11.2% to 41.2% and −15.6% to 44.9%, respectively. Similarly, under SSP370, the average monthly change in precipitation ranges from −3.6% to 36.4%, while the corresponding changes in streamflow and sediment yield range from −21.53% to 77.71% and −28.6% to 129.8%. Under SSP585, the average monthly change in precipitation ranges from −2.5% to 60.5%, while the corresponding changes in streamflow and sediment yield range from −15.8% to 134.4% and −21% to 166.5%. In the Nagavali and Vamsadhara watersheds, historical simulations indicate that 2438 and 5120 sq. km of basin areas, respectively, were subjected to high soil erosion. In contrast, under the far future Cold-Wet SSP585 scenario, 7468 and 9426 sq. km of basin areas in the Nagavali and Vamsadhara watersheds, respectively, are projected to experience high soil erosion. These results indicate that increased rainfall in the future (compared to the present) will lead to higher streamflow and sediment yield in both watersheds. This could have negative impacts on soil properties, agricultural lands, and reservoir capacity. Therefore, it is important to implement soil and water management practices in these river basins to reduce sediment loadings and mitigate these negative impacts.