This paper proposes a fully Bayesian approach for Least-Squares Temporal Differences (LSTD), resulting in fully probabilistic inference of value functions that avoids the overfitting commonly experienced with classical LSTD when the number of features is larger than the number of samples. Sparse Bayesian learning provides an elegant solution through the introduction of a prior over value function parameters. This gives us the advantages of probabilistic predictions, a sparse model, and good generalisation capabilities, as irrelevant parameters are marginalised out. The algorithm efficiently approximates the posterior distribution through variational inference. We demonstrate the ability of the algorithm in avoiding overfitting experimentally.