Mass loss from ice sheets under the ongoing anthropogenic warming episode is a major source for sea-level rise. Due to the slow responses of ice sheets to changes in atmospheric and oceanic boundary conditions, ice sheets are projected to undergo further retreat as the climate reaches a new equilibrium, producing a long-term commitment to future sea-level rise that is fulfilled on multi-millennial scale. Future projections of ice sheets beyond 2100 have routinely employed end-of-the-century atmosphere-ocean conditions from climate model output under specified emission scenarios. This approach, however, does not account for long-term responses of the climate system to external forcings. Here we analyze the long-term atmospheric and oceanic responses to a variety of emission scenarios in several climate models and show that polar climates may see substantial changes after the atmospheric CO2 level stabilizes. With a 3-D ice sheet model, we demonstrate that the long-term climate responses are crucial for evaluating ice sheets' commitment to future sea-level rise.