The cascade of uncertainty that underscores climate impact assessments of regional hydrology undermines their value for long-term water resources planning and management. This study presents a statistical framework that quantifies and propagates the uncertainties of hydrologic model response through projections of future streamflow under climate change. Different sources of hydrologic model uncertainty are accounted for using Bayesian modeling. The distribution of model residuals is formally characterized to quantify predictive skill, and Markov chain Monte Carlo sampling is used to infer the posterior distributions of both hydrologic and error model parameters. Parameter and residual error uncertainties are integrated to develop reliable prediction intervals for streamflow estimates. The Bayesian hydrologic modeling framework is then extended to a climate change impact assessment. Ensembles of baseline and future climate are downscaled from global circulation models and are used to drive simulations of streamflow over parameters drawn from the posterior space. Time series of streamflow statistics are calculated from baseline and future ensembles of simulated flows. Uncertainties in hydrologic model response, sampling error, and the range of future climate projections are integrated to help determine the level of confidence associated with hydrologic alteration between baseline and future climate regimes. A case study is conducted on the White River in Vermont, USA. Results indicate that the framework can be used to present a reliable depiction of the range of hydrologic alterations that may occur in the future.