Glacial terminations during the late Pleistocene epoch are associated with changes in insolation. They are also punctuated by millennial-scale climate shifts, characterized by a weakening and subsequent strengthening of the Atlantic meridional overturning circulation. This ubiquitous association suggests that these oscillations may be a necessary component of deglaciation. Model simulations have suggested that the period of weakened circulation during these terminal oscillations would be followed by an overshoot of the circulation on its resumption, but this phenomenon has not yet been observed. Here we use radiocarbon measurements of benthic foraminifera and carbonate preservation indices to reconstruct ventilation changes in the deep South Atlantic Ocean over the past 40,000 years. We find evidence for a particularly deep expansion of the Atlantic overturning cell directly following the weak mode associated with Heinrich Stadial 1. Our analysis of an ocean general circulation model simulation suggests that North Atlantic Deep Water export during the expansion was greater than that of interglacial conditions. We find a similar deep expansion during Dansgaard-Oeschger Interstadial Event 8, 38,000 years ago, which followed Heinrich Stadial 4. We conclude that the rise in atmospheric CO2 concentrations and resultant warming associated with an especially weak overturning circulation are sufficient to trigger a switch to a vigorous circulation, but a full transition to interglacial conditions requires additional forcing at an orbital scale.