Through 1959–2012, an airborne fraction (AF) of 0.44 of total anthropogenic CO₂ emissions remained in the atmosphere, with the rest being taken up by land and ocean CO₂ sinks. Understanding of this uptake is critical because it greatly alleviates the emissions reductions required for climate mitigation, and also reduces the risks and damages that adaptation has to embrace. An observable quantity that reflects sink properties more directly than the AF is the CO₂ sink rate (<i>k</i>_S), the combined land–ocean CO₂ sink flux per unit excess atmospheric CO₂ above preindustrial levels. Here we show from observations that <i>k</i>_S declined over 1959–2012 by a factor of about 1 / 3, implying that CO₂ sinks increased more slowly than excess CO₂. Using a carbon–climate model, we attribute the decline in <i>k</i>_S to four mechanisms: slower-than-exponential CO₂ emissions growth (~ 35% of the trend), volcanic eruptions (~ 25%), sink responses to climate change (~ 20%), and nonlinear responses to increasing CO₂, mainly oceanic (~ 20%). The first of these mechanisms is associated purely with the trajectory of extrinsic forcing, and the last two with intrinsic, feedback responses of sink processes to changes in climate and atmospheric CO₂. Our results suggest that the effects of these intrinsic, nonlinear responses are already detectable in the global carbon cycle. Although continuing future decreases in <i>k</i>_S will occur under all plausible CO₂ emission scenarios, the rate of decline varies between scenarios in non-intuitive ways because extrinsic and intrinsic mechanisms respond in opposite ways to changes in emissions: extrinsic mechanisms cause <i>k</i>_S to decline more strongly with increasing mitigation, while intrinsic mechanisms cause <i>k</i>_S to decline more strongly under high-emission, low-mitigation scenarios as the carbon–climate system is perturbed further from a near-linear regime.