Abstract The spread in projected global warming across the Coupled Model Intercomparison Project (CMIP) models under idealized forcing has been statistically linked to the inter‐model difference in climatological Atlantic Meridional Overturning Circulation (cAMOC), yet the underlying physical mechanisms remain unclear. Here, we analyze realistic future scenarios in CMIP models using a zero‐layer energy balance model (EBM) to establish a physical connection between cAMOC and future global warming. We find that enabled by weak stratification, a stronger cAMOC is associated with stronger ocean heat uptake efficiency and more negative climate feedbacks. Incorporating this connection into the zero‐layer EBM reveals an inverse relationship between cAMOC and future global warming. Applying the observed AMOC strength to this relationship constrains the 95% confidence interval of future sea surface warming from 0.51°C–2.25°C, 0.89°C–3.23°C, and 1.74°C–5.49°C to 0.83°C–2.19°C, 1.53°C–3.05°C, and 2.97°C–5.10°C under low‐ to high‐emission scenarios, respectively.