In recent decades, the ocean CO2 uptake has increased in response to rising atmospheric CO2. Yet, physical climate change also affects the ocean CO2 uptake, but magnitude and driving processes are poorly understood. Using a global ocean biogeochemistry model, we find that without climate change, the mean carbon uptake 2000–2019 would have been 13% higher and the trend 1958–2019 would have been 27% higher. Changes in wind are the dominant driver of the climate effect on CO2 uptake as they affect advective carbon transport and mixing, but the effect of warming increases over time. Roughly half of the globally integrated wind-driven trend stems from the subpolar Southern Ocean and polar oceans in both hemispheres. Warming reduces the solubility of CO2 and acts rather homogeneously over the world oceans. However, the warming effect on pCO2 is dampened by limited exchange of surface and deep waters.