The ocean moderates global warming by absorbing most of the excess heat resulting from anthropogenic climate change. However, this ocean heat uptake also causes sea level rise, more frequent extreme events, ocean deoxygenation, and multiple impacts on marine ecosystems. Despite their importance for informing climate mitigation and adaptation measures, ocean heat uptake projections still strongly differ between climate models. Here, we provide improved global ocean heat uptake projections by identifying a relationship between present-day Antarctic sea ice extent and future ocean heat uptake across an ensemble of 28 state-of-the-art climate models. Models with a higher present-day sea ice extent also simulate greater sea ice loss over the 21st century, a stronger global cloud feedback and atmospheric warming, and hence increased ocean heat uptake. By combining this relationship with satellite observations of Antarctic sea ice, we reduce the uncertainty of ocean heat uptake projections under realistic future emissions scenarios by 12-33%, and show that models underestimate present-day sea ice extent and consequently future ocean heat uptake by 5-7%. Our findings indicate that accounting for biases in the Southern Ocean mean state in the latest generation of climate models implies larger future climate warming.