The ocean is a vast store of anthropogenic and natural carbon, the former from manmade CO₂ emissions absorbed at the surface and the latter produced in the interior from remineralization of sinking biogenic particles. On the one hand, climate change is projected to decrease uptake, while on the other it is predicted to increase accumulation of regenerated carbon. However, for how long this carbon will remain sequestered in the ocean under a warming climate remains poorly constrained. Here, I quantify the impact of climate change on the sequestration efficiency of the ocean by computing the distribution of times and spatial locations at which carbon currently stored in the ocean is exposed to and exchanges with the atmosphere. These novel calculations fully take into account the time-evolving circulation and buffer chemistry of the ocean under a range of emission scenarios. I show that a projected increase in stratification and concomitant slowdown in the global overturning circulation due to global warming lengthens by centuries to thousands of years the time for which carbon remains sequestered. Moreover, this increase in storage time is evident even under low emission, high mitigation scenarios. The delay in reemergence of carbon at the surface reduces the impact on both future CO₂ uptake, via its effect on buffer chemistry, and climate, through outgasing into the atmosphere. The increase in sequestration efficiency is accompanied by a shift toward more circuitous and diffusive circulation pathways that further enhances the dominance of the Southern Ocean as the location at which the accumulated carbon outgases into the atmosphere. These results highlight the potential long-term impact of global warming-induced changes in the marine carbon cycle on climate.