Understanding the oceanic uptake of carbon from the atmosphere is essential for better constraining the global budget, as well as for predicting the air-borne fraction of CO2 emissions and thus degree of climate change. Gaining this understanding is difficult, because the 'natural' carbon cycle, the part of the global carbon cycle unaltered by CO2 emissions, also responds to climate change and ocean acidification. Using a global climate model of intermediate complexity, we assess the evolution of the natural carbon cycle over the next few centuries. We find that physical mechanisms, particularly Atlantic meridional overturning circulation and gas solubility, alter the natural carbon cycle the most and lead to a significant reduction in the overall oceanic carbon uptake. Important biological mechanisms include reduced organic carbon export production due to reduced nutrient supply, increased organic carbon production due to higher temperatures and reduced CaCO3 production due to increased ocean acidification. A large ensemble of model experiments indicates that the most important source of uncertainty in ocean uptake projections in the near term future are the upper ocean vertical diffusivity and gas exchange coefficient. By year 2300, the model's climate sensitivity replaces these two and becomes the dominant factor as global warming continues.