It is difficult to project sea-level rise in response to warming climates by the end of the century, especially because the response of the Greenland and Antarctic ice sheets to warming is not well understood1. However, sea-level fluctuations in response to changing climate have been reconstructed for the past 22,000 years from fossil data, a period that covers the transition from the Last Glacial Maximum to the warm Holocene interglacial period. Here we present a simple model of the integrated sea-level response to temperature change that implicitly includes contributions from the thermal expansion and the reduction of continental ice. Our model explains much of the centennial-scale variability observed over the past 22,000 years, and estimates 4–24 cm of sea-level rise during the twentieth century, in agreement with the Fourth Assessment Report of the Intergovernmental Panel on Climate Change1 (IPCC). In response to the minimum (1.1 °C) and maximum (6.4 °C) warming projected for AD 2100 by the IPCC models, our model predicts 7 and 82 cm of sea-level rise by the end of the twenty-first century, respectively. The range of sea-level rise is slightly larger than the estimates from the IPCC models of 18–76 cm, but is sufficiently similar to increase confidence in the projections.