The dominant feature of large-scale mass transfer in the modern ocean is the Atlantic meridional overturning circulation (AMOC). The geometry and vigour of this circulation influences global climate on various timescales. Palaeoceanographic evidence suggests that during glacial periods of the past 1.5 million years the AMOC had markedly different features from today; in the Atlantic basin, deep waters of Southern Ocean origin increased in volume while above them the core of the North Atlantic Deep Water (NADW) shoaled. An absence of evidence on the origin of this phenomenon means that the sequence of events leading to global glacial conditions remains unclear. Here we present multi-proxy evidence showing that northward shifts in Antarctic iceberg melt in the Indian–Atlantic Southern Ocean (0–50°E) systematically preceded deep-water mass reorganizations by one to two thousand years during Pleistocene-era glaciations. With the aid of iceberg-trajectory model experiments, we demonstrate that such a shift in iceberg trajectories during glacial periods can result in a considerable redistribution of freshwater in the Southern Ocean. We suggest that this, in concert with increased sea-ice cover, enabled positive buoyancy anomalies to ‘escape’ into the upper limb of the AMOC, providing a teleconnection between surface Southern Ocean conditions and the formation of NADW. The magnitude and pacing of this mechanism evolved substantially across the mid-Pleistocene transition, and the coeval increase in magnitude of the ‘southern escape’ and deep circulation perturbations implicate this mechanism as a key feedback in the transition to the ‘100-kyr world’, in which glacial–interglacial cycles occur at roughly 100,000-year periods.