We combine physics-based groundwater reactive transport modeling with machine learning techniques to quantify hydrogeologic model and solute transport predictive uncertainties. We train an artificial neural network (ANN) on a dataset of groundwater hydraulic heads and 3H concentrations generated using a high-fidelity groundwater reactive transport model. Using the trained ANN as a surrogate model to reproduce the input-output response of the high-fidelity reactive transport model, we quantify the posterior distributions of hydrogeologic parameters and hydraulic forcing conditions using Markov-chain Monte Carlo (MCMC) calibration against field observations of groundwater hydraulic heads and 3H concentrations. We demonstrate the methodology with a model application that predicts Chlorofluorocarbon-12 (CFC-12) solute transport at a contaminated site in Wyoming, USA. Our results show that including 3H observations in the calibration dataset reduced the uncertainty in the estimated permeability field and infiltration rates, compared to calibration against hydraulic heads alone. However, predictive uncertainty quantification shows that CFC-12 transport predictions conditioned to the parameter posterior distributions cannot reproduce the field measurements. We found that calibrating the model to hydraulic head and 3H observations results in groundwater mean ages that are too large to explain the observed CFC-12 concentrations. The coupling of the physics-based reactive transport model with the machine learning surrogate model allows us to efficiently quantify model parameter and predictive uncertainties, which is typically computationally intractable using reactive transport models alone.