We examine the link between migrations in the intertropical convergence zone (ITCZ) and changes in the Atlantic meridional overturning circulation (AMOC), Atlantic multidecadal variability (AMV), and Pacific decadal oscillation (PDO). We use a coupled climate model that allows us to integrate over climate noise and assess underlying mechanisms. We use an ensemble of ten 300-yr-long simulations forced by a 50-yr oscillatory North Atlantic Oscillation (NAO)-derived surface heat flux anomaly in the North Atlantic, and a 4000-yr-long preindustrial control simulation performed with GFDL CM2.1. In both setups, an AMV phase change induced by a change in the AMOC’s cross-equatorial heat transport forces an atmospheric interhemispheric energy imbalance that is compensated by a change in the cross-equatorial atmospheric heat transport due to a meridional ITCZ shift. Such linkages occur on decadal time scales in the ensemble driven by the imposed forcing, and internally on multicentennial time scales in the control. Regional precipitation anomalies differ between the ensemble and the control for a zonally averaged ITCZ shift of similar magnitude, which suggests a dependence on time scale. Our study supports observational evidence of an AMV–ITCZ link in the twentieth century and further links it to the AMOC, whose long-time-scale variability can influence the phasing of ITCZ migrations. In contrast to the AMV, our calculations suggest that the PDO does not drive ITCZ migrations, because the PDO does not modulate the interhemispheric energy balance.