Extreme, abrupt Northern Hemisphere climate oscillations during the last glacial cycle (140,000 years ago to present) were modulated by changes in ocean circulation and atmospheric forcing1. However, the variability of the Atlantic meridional overturning circulation (AMOC), which has a role in controlling heat transport from low to high latitudes and in ocean CO2 storage, is still poorly constrained beyond the Last Glacial Maximum2, 3, 4. Here we show that a deep and vigorous overturning circulation mode has persisted for most of the last glacial cycle, dominating ocean circulation in the Atlantic, whereas a shallower glacial mode with southern-sourced waters filling the deep western North Atlantic prevailed during glacial maxima3, 5. Our results are based on a reconstruction of both the strength and the direction of the AMOC during the last glacial cycle from a highly resolved marine sedimentary record in the deep western North Atlantic. Parallel measurements of two independent chemical water tracers (the isotope ratios of 231Pa/230Th and 143Nd/144Nd)6, 7, 8, which are not directly affected by changes in the global cycle, reveal consistent responses of the AMOC during the last two glacial terminations. Any significant deviations from this configuration, resulting in slowdowns of the AMOC, were restricted to centennial-scale excursions during catastrophic iceberg discharges of the Heinrich stadials. Severe and multicentennial weakening of North Atlantic Deep Water formation occurred only during Heinrich stadials close to glacial maxima with increased ice coverage, probably as a result of increased fresh-water input. In contrast, the AMOC was relatively insensitive to submillennial meltwater pulses during warmer climate states, and an active AMOC prevailed during Dansgaard–Oeschger interstadials (Greenland warm periods).