The links between the atmospheric southern annular mode (SAM), the Southern Ocean, and the Atlantic meridional overturning circulation (AMOC) at interannual to multidecadal time scales are investigated in a 500-yr control integration of the L'Institut Pierre-Simon Laplace Coupled Model, version 4 (IPSL CM4) climate model. The Antarctic Circumpolar Current, as described by its transport through the Drake Passage, is well correlated with the SAM at the yearly time scale, reflecting that an intensification of the westerlies south of 45°S leads to its acceleration. Also in phase with a positive SAM, the global meridional overturning circulation is modified in the Southern Hemisphere, primarily reflecting a forced barotropic response. In the model, the AMOC and the SAM are linked at several time scales. An intensification of the AMOC lags a positive SAM by about 8 yr. This is due to a correlation between the SAM and the atmospheric circulation in the northern North Atlantic that reflects a symmetric ENSO influence on the two hemispheres, as well as an independent, delayed interhemispheric link driven by the SAM. Both effects lead to an intensification of the subpolar gyre and, by salinity advection, increased deep convection and a stronger AMOC. A slower oceanic link between the SAM and the AMOC is found at a multidecadal time scale. Salinity anomalies generated by the SAM enter the South Atlantic from the Drake Passage and, more importantly, the Indian Ocean; they propagate northward, eventually reaching the northern North Atlantic where, for a positive SAM, they decrease the vertical stratification and thus increase the AMOC.