A central question in reinforcement learning (RL) is how to leverage prior knowledge to accelerate learning in new tasks. We propose a Bayesian exploration method for lifelong reinforcement learning (BLRL) that aims to learn a Bayesian posterior that distills the common structure shared across different tasks. We further derive a sample complexity analysis of BLRL in the finite MDP setting. To scale our approach, we propose a variational Bayesian Lifelong Learning (VBLRL) algorithm that is based on Bayesian neural networks, can be combined with recent model-based RL methods, and exhibits backward transfer. Experimental results on three challenging domains show that our algorithms adapt to new tasks faster than state-of-the-art lifelong RL methods.