The Southern Ocean has shown little warming over recent decades, in stark contrast to the rapid warming observed in the Arctic. Along the northern flank of the Antarctic Circumpolar Current, however, the upper ocean has warmed substantially. Here we present analyses of oceanographic observations and general circulation model simulations showing that these patterns—of delayed warming south of the Antarctic Circumpolar Current and enhanced warming to the north—are fundamentally shaped by the Southern Ocean’s meridional overturning circulation: wind-driven upwelling of unmodified water from depth damps warming around Antarctica; greenhouse gas-induced surface heat uptake is largely balanced by anomalous northward heat transport associated with the equatorward flow of surface waters; and heat is preferentially stored where surface waters are subducted to the north. Further, these processes are primarily due to passive advection of the anomalous warming signal by climatological ocean currents; changes in ocean circulation are secondary. These findings suggest the Southern Ocean responds to greenhouse gas forcing on the centennial, or longer, timescale over which the deep ocean waters that are upwelled to the surface are warmed themselves. It is against this background of gradual warming that multidecadal Southern Ocean temperature trends must be understood.