Warming of the North Atlantic region in climate history often was associated with massive melting of the Greenland Ice Sheet. To identify the meltwater's impacts and isolate these from internal variability and other global warming factors, we run single-forcing simulations including small ensembles using three complex climate models differing only in their ocean components. In 200-year-long preindustrial climate simulations, we identify robust consequences of abruptly increasing Greenland runoff by 0.05 Sv: sea level rise of 44 ± 10 cm, subpolar North Atlantic surface cooling of 0.7°C, and a moderate AMOC decline of 1.1–2.0 Sv. The latter two emerge in under three decades—and reverse on the same timescale after the perturbation ends in year 100. The ocean translates the step-change perturbation into a multidecadal-to-centennial signature in the deep overturning circulation. In all simulations, internal variability creates notable uncertainty in estimating trends, time of emergence, and duration of the response.