By absorbing large amounts of anthropogenic carbon from the atmosphere, the ocean strongly buffers the magnitude of warming caused by CO<sub>2</sub> emissions. This ocean carbon uptake is often conceptually separated into two components, quantified by the feedback parameters β and γ: The uptake of anthropogenic CO<sub>2</sub> driven by rising atmospheric concentration (β), and the effect of climate warming (γ), which reduces this anthropogenic uptake and drives a loss of natural carbon already stored in the ocean. Together, β and γ determine how effectively the ocean absorbs CO<sub>2</sub> emissions and shape how much emitted carbon remains in the atmosphere. Thus, β and γ directly affect how much the climate system warms in response to emitted carbon, i.e., the transient climate response to cumulative CO<sub>2</sub> emissions (TCRE). However, estimates of ocean β and γ from Earth system models differ widely, leading to substantial uncertainty in the TCRE.</p> <p>Here, we extend and apply a previously identified emergent constraint linking ocean anthropogenic carbon uptake to observable indicators of the formation of Southern Ocean mode and intermediate waters, North Atlantic deep water formation, and the global surface ocean chemical uptake capacity. In addition to these three predictors, we add an additional indicator for bottom water formation via open-ocean deep convection, defined as the volume of waters below 3000 m that is ventilated via extremely deep mixed layer depths. Using observations of these four indicators, the constrained β is 0.96±0.05 Pg C ppm−1 at doubling of atmospheric CO<sub>2</sub> and 0.85±0.04 Pg C ppm−1 at quadrupling of atmospheric CO<sub>2</sub>. The observationally constrained β is around 4-5% larger and around 35-47% less uncertain than previously estimated. This larger ocean β is further supported by simulated historical anthropogenic carbon uptake in most models being lower than observation-based estimates,<br />although uncertainties in the latter remain too large to directly constrain β.</p> <p>Beyond constraining ocean β, we show that ocean β and γ become increasingly correlated over time. This relationship emerges because models with higher anthropogenic carbon uptake, and hence larger β, also show a stronger suppression of that uptake in response to climate change. The stronger suppression is driven by a larger reduction in the indicators for ocean carbon uptake identified above in models with higher indicators at the beginning of the simulations, e.g., a model with stronger ventilation at present will also see a stronger reduction of that ventilation in the future. As atmospheric CO<sub>2</sub> increases, the climate-driven reduction in anthropogenic carbon uptake increasingly dominates over the climate-driven loss of natural carbon, causing γ to become primarily controlled by reductions in anthropogenic carbon uptake over time. As a result, the same observable indicators that constrain ocean β also constrain ocean γ at high CO<sub>2</sub>. At doubling of atmospheric CO<sub>2</sub>, this yields a constrained ocean γ of -10.1±2.4 Pg C ◦C−1, which is 23% larger in magnitude but has the same uncertainty as<br />the unconstrained multi-model mean. Reflecting the strengthening of this relationship with increasing atmospheric CO<sub>2</sub>, the constraint tightens further at quadrupling of CO<sub>2</sub> to -24.5±3.6 Pg C °C−1, which is 28% larger and 42% less uncertain.</p> <p>Overall, we have extended a previous constraint for the ocean carbon uptake by (1) adding an additional parameter that removed a known bias from unrealistic open-ocean deep convection, (2) transferring the constraint to γ and providing a mechanistical explanation for that constraint and evidence for that mechanism, (3) applying the constraint regionally, (4) identifying substantial biases in β and γ and reducing uncertainties, and (5) improving process understanding of drivers of changes in the ocean carbon sink. Although both the increase in atmospheric CO<sub>2</sub> uptake and the increase in carbon loss with climate change were biased across the model ensembles and could be constrained, the bias corrections of β and γ offset each other, leaving the best estimate of the ocean carbon sink relatively unchanged (2–3% increase compared to this ensemble mean). However, the uncertainties of β and γ are reduced and hence is the overall uncertainty of the carbon sink, which will propagate into smaller uncertainties of important climate metrics such as the TCRE.