The fundamental role of the hydrological cycle in the global climate system motivates a thorough evaluation of its responses to climate change and mitigation. The Geoengineering Model Intercomparison Project (GeoMIP) is a coordinated international effort to assess the climate impacts of solar geoengineering, a proposal to counteract global warming with a reduction in incoming solar radiation. We assess the mechanisms underlying the rainfall response to a simplified simulation of such solar dimming (G1) in the suite of GeoMIP models and identify robust features. While solar geoengineering nearly restores preindustrial temperatures, the global hydrology is altered. Tropical precipitation changes dominate the response across the model suite, and these are driven primarily by shifts of the Hadley circulation cells. We report a damping of the seasonal migration of the Intertropical Convergence Zone (ITCZ) in G1, associated with preferential cooling of the summer hemisphere, and annual mean ITCZ shifts in some models that are correlated with the warming of one hemisphere relative to the other. Dynamical changes better explain the varying tropical rainfall anomalies between models than changes in relative humidity or the Clausius–Clapeyron scaling of precipitation minus evaporation (P − E), given that the relative humidity and temperature responses are robust across the suite. Strong reductions in relative humidity over vegetated land regions are likely related to the CO₂ physiological response in plants. The uncertainty in the spatial distribution of tropical P − E changes highlights the need for cautious consideration and continued study before any implementation of solar geoengineering.