In this study, an efficient full Bayesian approach was developed for the optimal sampling well design and source identification of groundwater contaminants. An information measure, i.e., the relative entropy, was employed to quantify the information gain from indirect concentration measurement in identifying unknown source parameters including the release time, strength, and location of the contaminant. In the approach, the sampling location which gives the maximum relative entropy was selected as the optimal one. Once the sampling location was determined, a Bayesian approach based on Markov Chain Monte Carlo (MCMC) was used to estimate the unknown source parameters. In both the design and estimation, the contaminant transport equation is required to be solved many times to evaluate the likelihood. To reduce the computational burden, an interpolation based on the adaptive sparse grid was utilized to construct a surrogate for the contaminant transport. The approximated likelihood was evaluated directly from the surrogate. The accuracy and efficiency of this method were demonstrated through numerical case studies. The approach used in this study greatly accelerates the sampling design and parameter estimation processe and the proposed method can be used to assist in monitor network design and identification of unknown contaminant sources.