In recent decades, the rise in atmospheric CO2 has caused an increase in oceanic CO2 uptake. Yet, climate change and variability also affect the air-sea CO2 flux, which is less well understood. We use a global ocean biogeochemistry model to quantify these effects from 1958-2019. Our simulations show that, on average during 2000-2019, the ocean took up 2 PgC yr-1 more than in its preindustrial state, corresponding to a trend of 24 TgC yr-2 from 1958-2019. Climate effects reduced the mean flux 2000-2019 by 13% and the trend 1958-2019 by 26%. The most important drivers were winds (mean: 9%, trend: 12%) and sea surface warming (mean: 5%, trend: 10%). Winds reduced the oceanic CO2 uptake largely through changes in the carbon transport with the ocean circulation. Warming primarily drove a reduced solubility of natural CO2 where the exchange of surface and deep waters determines the magnitude of this effect.