As the ocean absorbs 25% of the anthropogenic emissions of carbon, it is important to understand the impact of climate change on the flux of carbon between the ocean and the atmosphere. Here, we use a very high-resolution ocean, sea-ice, carbon cycle model to show that the capability of the Southern Ocean to uptake CO₂ has decreased over the last 40 years due to a strengthening and poleward shift of the southern hemispheric westerlies. This trend is expected to continue over the coming century.