The Atlantic Meridional Overturning Circulation is the main driver of northward heat transport in the Atlantic Ocean today, setting global climate patterns. Whether global warming has affected the strength of this overturning circulation over the past century is still debated: observational studies suggest that there has been persistent weakening since the mid-twentieth century, whereas climate models systematically simulate a stable circulation. Here, using Earth system and eddy-permitting coupled ocean–sea-ice models, we show that a freshening of the subarctic Atlantic Ocean and weakening of the overturning circulation increase the temperature and salinity of the South Atlantic on a decadal timescale through the propagation of Kelvin and Rossby waves. We also show that accounting for upper-end meltwater input in historical simulations significantly improves the data–model agreement on past changes in the Atlantic Meridional Overturning Circulation, yielding a slowdown of 0.46 sverdrups per decade since 1950. Including estimates of subarctic meltwater input for the coming century suggests that this circulation could be 33% weaker than its anthropogenically unperturbed state under 2 °C of global warming, which could be reached over the coming decade. Such a weakening of the overturning circulation would substantially affect the climate and ecosystems. Fresh meltwater entering the Labrador and Irminger seas has resulted in a slowing of the Atlantic Meridional Overturning Circulation since the 1950s, according to a combination of modelling approaches.