Global mean sea level has been steadily rising over the last century, is projected to increase by the end of this century, and will continue to rise beyond the year 2100 unless the current global mean temperature trend is reversed. Inertia in the climate and global carbon system, however, causes the global mean temperature to decline slowly even after greenhouse gas emissions have ceased, raising the question of how much sea-level commitment is expected for different levels of global mean temperature increase above preindustrial levels. Although sea-level rise over the last century has been dominated by ocean warming and loss of glaciers, the sensitivity suggested from records of past sea levels indicates important contributions should also be expected from the Greenland and Antarctic Ice Sheets. Uncertainties in the paleo-reconstructions, however, necessitate additional strategies to better constrain the sea-level commitment. Here we combine paleo-evidence with simulations from physical models to estimate the future sea-level commitment on a multimillennial time scale and compute associated regional sea-level patterns. Oceanic thermal expansion and the Antarctic Ice Sheet contribute quasi-linearly, with 0.4 m °C-1 and 1.2 m °C-1 of warming, respectively. The saturation of the contribution from glaciers is overcompensated by the nonlinear response of the Greenland Ice Sheet. As a consequence we are committed to a sea-level rise of approximately 2.3 m °C-1 within the next 2,000 y. Considering the lifetime of anthropogenic greenhouse gases, this imposes the need for fundamental adaptation strategies on multicentennial time scales.