While previous studies have suggested that the Atlantic Meridional Overturning Circulation (AMOC) weakens under greenhouse warming, large uncertainties remain regarding what drives the intermodel differences in the weakening of AMOC decadal variability and its associated physical mechanisms. Using simulations from a suite of CMIP6 models, we show that AMOC decadal variability substantially weakens from the historical period to the SSP245 scenario, mainly driven by greenhouse gas forcing. These changes in the decadal AMOC variability are largely attributable to the variations in mixed layer depth (MLD) across the subpolar basins and to the mean AMOC state. Across models, the magnitude of the reduction in AMOC decadal variance is strongly positively correlated with the AMOC strength. Models with a stronger mean-state AMOC preferentially form deep convection in the Labrador Sea, whereas those with a weaker mean-state AMOC exhibit deep convection closer to the Nordic Seas, highlighting the critical role of deep-convection location in controlling the future reduction of AMOC decadal variability. Our results highlight the necessity of an improved representation of AMOC mean state and deep convection position for reducing uncertainties in future AMOC projections and associated climate impacts.