The Atlantic meridional overturning circulation (AMOC) is an important component of the climate system because of the associated heat and freshwater transports. Global warming is projected to weaken the AMOC by up to 50% towards the end of the 21st century. Here we show a delayed aspect of climate change, linked to AMOC changes, in an idealised scenario of greenhouse-gas-increase and subsequent mitigation as projected by two comprehensive coupled climate models. Under an imposed increase in CO2, there is a reduction in meridional exchange of ocean waters due to the associated weakening AMOC, and an intensification of the hydrological cycle, which result in a tendency to increase salinity in the subtropics and to freshen the northern latitudes. The AMOC and meridional ocean transports recover during the subsequent mitigation phase. As the reservoir of very warm and saline water previously built up in the subtropics is transported northwards, a consequent massive increase of salinity in the Arctic/subpolar North Atlantic results in large density increases in the deep water formation regions. This drives an overshoot in the strength of the AMOC by 30–100% relative to its pre-industrial strength. This AMOC overshoot gives an extended period of anomalously strong northward heat transport, maintaining warmer northern high latitudes for decades after the atmospheric CO2 concentration returns to preindustrial values. This work demonstrates the important role of coupling between the hydrological cycle and large scale ocean dynamics in future climate change, and that some aspects of currently committed climate change have yet to be revealed.