The dynamics of Northern Hemisphere ice sheets during Late Quaternary glacials have yet been dominantly examined from a Laurentide Ice Sheet perspective, which helped shaping the idea of moisture-starved glacials and small-scale ice volume variability. However, the waxing and waning of the European Ice Sheet (EIS) casts doubt on this perception. Understanding EIS dynamics under glacial boundary conditions is crucial because its meltwater pulses influence global climate by weakening deepwater formation in the North Atlantic Ocean. Here we show that the advection of subtropical water toward the continental margin of western Europe lead to enhanced moisture availability on the continent and fueled the growth of EIS lobes during glacials. This warm-water pooling was caused by monsoonally paced enhanced Mediterranean Outflow Water (MOW) entrainment that dragged subtropical surface waters toward the European margin. This mechanism presents a yet unrecognized marine-terrestrial pathway that allows low-latitude forcing to shape high-latitude glaciations. Plain Language Summary The build-up of glacial ice shields required large amounts of atmospheric precipitating as snow. However, under full glacial conditions, cold surface oceans reduce the amount of evaporation, which counteracts the growth of large continental ice shields. Our study aims to unravel the source and transport pathways of moisture that helped to rapidly form the European Ice Shield during the past two glacials. We propose the novel concept that the outflow of dense Mediterranean water into the North Atlantic played a decisive role as it helped to "drag" warm surface waters toward the European Margin by strengthening the Azores Current. This warm, subtropical water current supplied vast amounts of moisture, which then was transported northward into continental Europe and fueled ice sheet growth. The strength of Mediterranean Outflow Water discharge into the Atlantic strongly depends on monsoonal activity in its source region in the Eastern Mediterranean Sea. Thus, warm water advection toward western Europe and associated glacier growth of the European Ice Shield are intimately linked to low-latitude climate changes, closely following the similar to 21 kyr beat of orbital precession.