In climate model simulations of future climate change, the Atlantic Meridional Overturning Circulation (AMOC) is projected to decline. However, the impacts of this decline, relative to other changes, remain to be identified. Here we address this problem by analyzing 30 idealized abrupt-4xCO2 climate model simulations. We find that in models with larger AMOC decline, there is a minimum warming in the North Atlantic, a southward displacement of the Inter-tropical Convergence Zone, and a poleward shift of the mid-latitude jet. The changes in the models with smaller AMOC decline are drastically different: there is a relatively larger warming in the North Atlantic, the precipitation response exhibits a wet-get-wetter, dry-get-drier pattern, and there are smaller displacements of the mid-latitude jet. Our study indicates that the AMOC is a major source of inter-model uncertainty, and continued observational efforts are needed to constrain the AMOC response in future climate change.