Volcanic aerosols reduce global mean precipitation in the years after major eruptions, yet the mechanisms that produce this response have not been rigorously identified. Volcanic aerosols alter the atmosphere's energy balance, with precipitation changes being one pathway by which the atmosphere acts to return towards equilibrium. By assessing the atmosphere's energy budget in climate model simulations, we here show that global precipitation reduction is largely a consequence of Earth's surface cooling in response to volcanic aerosols reflecting incoming sunlight. In addition, these aerosols also directly add energy to the atmosphere by absorbing outgoing longwave radiation, and this is a major cause of precipitation decline in the first post-eruption year. We also identify mechanisms that oppose the post-eruption precipitation decline, and provide evidence that our results are robust across climate models.