Reducing uncertainty in the response of the Amazon rainforest, a vital component of the Earth system, to future climate change is crucial for refining climate projections. Here we demonstrate an emergent constraint (EC) on the future response of the Amazon carbon cycle to climate change across CMIP6 Earth system models. Models that overestimate past global warming trends, tend to estimate hotter and drier future Amazon conditions, driven by northward shifts of the intertropical convergence zone over the Atlantic Ocean, causing greater Amazon carbon loss. The proposed EC changes the mean CMIP6 Amazon climate-induced carbon loss estimate (excluding CO2 fertilisation and land-use change impacts) from −0.27 (−0.59–0.05) to −0.16 (−0.42–0.10) GtC year−1 at 4.4 °C warming level, reducing the variance by 34%. This study implies that climate-induced carbon loss in the Amazon rainforest by 2100 is less than thought and that past global temperature trends can be used to refine regional carbon cycle projections.