The upper branch of the Atlantic Meridional Overturning Circulation (AMOC) plays a critical role in ocean circulation and climate change, yet its variability during the last glacial period is poorly documented. Here, we investigate the northward‐flowing Glacial Eastern Boundary Current (GEBC) in the North Atlantic, known today as the European Slope Current, and representing the easternmost portion of the upper branch of the AMOC. Based on flow speed and isotopic records, we show that Dansgaard‐Oeschger (D/O) interstadials (stadials) correspond to a faster (weaker) GEBC during the ∼50‐15 ka period. This, by analogy to present‐day conditions, suggests enhanced (reduced) strength of the subpolar gyre and, by extension, of northern‐sourced water production and AMOC during D‐O interstadials (stadials). Concomitant fluctuations of both the GEBC and the European Ice Sheet between ∼30 and 17 ka suggest an active role of the upper branch of AMOC in the poleward transport of heat and freshwater to the northern North Atlantic, with direct impacts on deep water formation and AMOC strength. We explore these ice‐sheet ‐ AMOC interactions and the associated abrupt climate changes over the last glacial period and the last deglaciation.