The processes controlling the carbon flux and carbon storage of the atmosphere, ocean and terrestrial biosphere are temperature sensitive and are likely to provide a positive feedback leading to amplified anthropogenic warming. Owing to this feedback, at timescales ranging from interannual to the 20-100-kyr cycles of Earth's orbital variations, warming of the climate system causes a net release of CO(2) into the atmosphere; this in turn amplifies warming. But the magnitude of the climate sensitivity of the global carbon cycle (termed gamma), and thus of its positive feedback strength, is under debate, giving rise to large uncertainties in global warming projections. Here we quantify the median gamma as 7.7 p.p.m.v. CO(2) per degrees C warming, with a likely range of 1.7-21.4 p.p.m.v. CO(2) per degrees C. Sensitivity experiments exclude significant influence of pre-industrial land-use change on these estimates. Our results, based on the coupling of a probabilistic approach with an ensemble of proxy-based temperature reconstructions and pre-industrial CO(2) data from three ice cores, provide robust constraints for gamma on the policy-relevant multi-decadal to centennial timescales. By using an ensemble of >200,000 members, quantification of gamma is not only improved, but also likelihoods can be assigned, thereby providing a benchmark for future model simulations. Although uncertainties do not at present allow exclusion of gamma calculated from any of ten coupled carbon-climate models, we find that gamma is about twice as likely to fall in the lowermost than in the uppermost quartile of their range. Our results are incompatibly lower (P < 0.05) than recent pre-industrial empirical estimates of approximately 40 p.p.m.v. CO(2) per degrees C (refs 6, 7), and correspondingly suggest approximately 80% less potential amplification of ongoing global warming.