The ocean has absorbed 41 per cent of all anthropogenic carbon emitted as a result of fossil fuel burning and cement manufacture. The magnitude and the large-scale distribution of the ocean carbon sink is well quantified for recent decades. In contrast, temporal changes in the oceanic carbon sink remain poorly understood. It has proved difficult to distinguish between air-to-sea carbon flux trends that are due to anthropogenic climate change and those due to internal climate variability. Here we use a modelling approach that allows for this separation, revealing how the ocean carbon sink may be expected to change throughout this century in different oceanic regions. Our findings suggest that, owing to large internal climate variability, it is unlikely that changes in the rate of anthropogenic carbon uptake can be directly observed in most oceanic regions at present, but that this may become possible between 2020 and 2050 in some regions.