Abstract Both the Greenland and Antarctic ice sheets have been melting at an accelerating rate over recent decades. Meltwater from Greenland might be expected to initiate a climate response that is distinct, and perhaps different from, that associated with Antarctic meltwater. Which one might elicit a greater climate response, and what mechanisms are involved? To explore these questions, we apply climate response functions (CRFs) to guide a series of meltwater-perturbation experiments using a fully coupled climate model. In both hemispheres, meltwater drives atmospheric cooling, sea ice expansion, and strengthened Hadley and Ferrel cells. Greenland meltwater induces a slowdown of the Atlantic meridional overturning circulation (AMOC) and a cooling of the subsurface ocean in the northern high latitudes. Antarctic meltwater, instead, induces a slowdown of the Antarctic Bottom Water formation and a warming of the subsurface ocean around Antarctica. For melt rates up to 2000 Gt yr−1, the climate response is rather linear. However, as melt rates increase to 5000 Gt yr−1, the climate response becomes nonlinear. Due to a collapsed AMOC, the climate response is superlinear at high Greenland melt rates. Instead, the climate response is sublinear at high Antarctic melt rates, due to the halting of the northward expansion of Antarctic sea ice by warm surface waters. Finally, in the linear limit, we use CRFs and linear convolution theory to make projections of important climate parameters in response to meltwater scenarios, which suggest that Antarctic meltwater will become a major driver of climate change, dominating that of Greenland meltwater, as the current century proceeds. Significance Statement Melting of the Greenland and Antarctic ice sheets is one of the most uncertain potential contributors to future climate change. In this study, we address the comparative role of Greenland and Antarctic meltwater in the climate system and explore the differing mechanisms at work in each hemisphere. We find that the climate response is linear for low melt rates but becomes nonlinear for high melt rates. As the century proceeds, we speculate that Antarctic meltwater will increasingly dominate that of Greenland meltwater, leading to atmospheric cooling, Antarctic sea ice expansion, and contraction and warming of the Antarctic Bottom Water. Greenland meltwater will, instead, affect smaller changes in the Northern Hemisphere.