Water isotope ratios in ice cores and marine sediments are a key indicator of past temperature and global ice volume. Quantitative interpretation of these ratios requires understanding of the storage capacity and exchanges among the ocean, atmosphere, and cryosphere. We combine numerical models of ice dynamics and tracer transport to predict bulk ice properties by simulating the fine layering of ice sheets locally validated at ice core sites. The O-18/O-16 content of ice sheets is found to vary between the present and 20 kyr ago from -34 parts per thousand to -37 parts per thousand for Greenland, from -41 parts per thousand to -42.5 parts per thousand for West Antarctica, and always remained near -56.5 parts per thousand for East Antarctica. Their combined effect on sea-water O-18/O-16 is a 0.08-0.12 parts per thousand increase 20 kyr ago, a 1.11 parts per thousand decrease if ice sheets were to vanish. We confirm that ice volume changes in Antarctica and Greenland linearly affect ocean composition, though at different rates.