During the last two deglaciations Southern Hemisphere warming preceded Greenland warming and the northern Atlantic has been exposed to meltwater discharge that is known to reduce North Atlantic deep water (NADW) formation. Yet, deglaciation is accompanied by a transition from a weak glacial to a strong interglacial Atlantic thermohaline circulation (THC). Here we utilize a three-dimensional ocean circulation model to investigate the impact of Southern Ocean warming and associated sea ice retreat onto the Atlantic THC. We show that gradual warming in the Southern Ocean induces an abrupt resumption of interglacial Atlantic THC by increased mass transport via the warm and cold water route of the global oceanic conveyor belt circulation. This effect prevails over the destabilizing effect of deglacial meltwater input to the northern Atlantic. The mechanism provides a consistent picture of Southern and Northern Hemisphere climate change in agreement with proxy records during deglaciation.