Current studies of the impact of climate change mitigation options tend to scale patterns of precipitation change linearly with surface temperature. Using climate model simulations, we show a nonlinear hydrological response to transient global warming and a substantial side effect of climate mitigation. In an idealised representation of mitigation action, where we reverse the trend of global warming, the precipitation response shows significant hysteresis behaviour due to heat previously accumulated in the ocean. Stabilising or reducing CO2 concentrations in the atmosphere is found temporarily to strengthen the global hydrological cycle, while reducing rainfall over some tropical and subtropical regions. The drying trend under global warming over The Amazon, Australia and western Africa may intensify for decades after CO2 reductions. The inertia due to accumulated heat in the ocean implies a commitment to hydrological cycle changes long after stabilisation or reduction of atmospheric CO2 concentration.