The IPSL‐CM6‐LR atmosphere‐ocean coupled model exhibits a pronounced multi‐centennial variability of the Atlantic meridional overturning circulation (AMOC), driven by delayed freshwater accumulation and release in the Arctic. The AMOC fluctuations are preceded by salinity‐driven density anomalies in the main deep convection sites in the Labrador and Greenland seas. During a strong AMOC, a combination of reduced sea‐ice volume and anomalous currents reduces the freshwater export from the Arctic and leads instead to a slow accumulation of freshwater in the central Arctic. Simultaneously, the saltier Atlantic inflow through the Barents Sea results in a positive salinity anomaly in the Eastern Arctic subsurface. When the surface Central Arctic freshwater pool finally reaches the Lincoln Sea, the oceanic currents around Greenland reorganize, leading to the export of the anomalous Arctic freshwater to the North Atlantic, enhancing the stratification in deep convection sites. The AMOC then decreases, positive salinity anomalies appear in the Central Arctic, and the variability switches to the opposite phase. These AMOC and sea ice fluctuations have broader climate impacts, with a strong AMOC leading to a mean warming of about 0.4°C north of 20°N, reaching up to 1°C in the Arctic lower troposphere during winter. In all seasons, a northward displacement of the intertropical convergence zone is also simulated.