The diffusion of hydrogen in MgB2 is crucial to the kinetics of rehydrogenation of Mg(BH4)2. We report a comprehensive combination of first-principles calculations and Kinetic Monte Carlo Simulations to examine the energetics of diffusion of hydrogen atoms through bulk MgB2. From these calculations we find that diffusion is fast for the neutral interstitial hydrogen defect and that the overall migration barrier for hydrogen diffusion in MgB2 is 0.22eV, showing that rapid diffusion of hydrogen is possible even at moderate temperatures. The interstitial hydrogen defect formation energy is around 0.8eV at 0K, indicating a low hydrogen solubility at moderate temperatures.