The observed mass loss from the West Antarctic Ice Sheet (WAIS) raises concerns about its stability1-4, since a collapse would raise global sea levels by several meters5. This mass loss is projected with ice sheet models that represent the present-day Antarctic ice sheet. We developed a new initialization method that optimizes agreement not only with ice thickness and surface velocity, but also with satellite-observed mass change rates. Starting from this initial state, we project future Antarctic mass changes while holding the ocean and atmospheric forcing constant at present-day values. We find that for a wide range of model settings, Thwaites Glacier and Pine Island Glacier collapse. The collapse is manifested by a slow retreat over several centuries followed by a significant speedup that lasts about 200 years. Our results imply that today’s mass loss rates are a precursor of the deglaciation of large parts of the WAIS, which would raise sea levels by at least a meter in the coming centuries, even without additional climate forcing.