We introduce and evaluate an eXplainable Goal Recognition (XGR) model that uses the Weight of Evidence (WoE) framework to explain goal recognition problems. Our model provides human-centered explanations that answer why? and why not? questions. We computationally evaluate the performance of our system over eight different domains. Using a human behavioral study to obtain the ground truth from human annotators, we further show that the XGR model can successfully generate human-like explanations. We then report on a study with 60 participants who observe agents playing Sokoban game and then receive explanations of the goal recognition output. We investigate participants' understanding obtained by explanations through task prediction, explanation satisfaction, and trust.