The fundamental role of the hydrological cycle in the global climate system motivates thorough evaluation of its responses to climate change and mitigation. The Geoengineering Model Intercomparison Project (GeoMIP) is a global collaboration that aims to assess the climate impacts of solar geoengineering, a proposal to counteract global warming with a reduction of incoming solar radiation. We assess the mechanisms underlying the rainfall response to a simplified simulation of solar dimming in the suite of GeoMIP models and identify robust features. While solar geoengineering restores preindustrial temperatures, the global hydrology is altered. Tropical precipitation changes dominate the response across the model suite. The models indicate a range of possibilities for the hydrological response, and in most cases, both thermodynamic and non-thermodynamic mechanisms drive precipitation minus evaporation changes in the geoengineered simulations relative to the preindustrial. Shifts of the Hadley circulation cells cause greater rainfall anomalies than local changes in relative humidity or the Clausius-Clapeyron scaling of precipitation minus evaporation. The variations among models in the movement of the intertropical convergence zone highlights the need for cautious consideration and continued study before any implementation of solar geoengineering.