We derive a constraint on the strength of CO₂ fertilisation of the terrestrial biosphere through a "top-down" approach, calibrating Earth system model parameters constrained by the post-industrial increase of atmospheric CO₂ concentration. We derive a probabilistic prediction for the globally averaged strength of CO₂ fertilisation in nature, for the period 1850 to 2000 AD, implicitly net of other limiting factors such as nutrient availability. The approach yields an estimate that is independent of CO₂ enrichment experiments. To achieve this, an essential requirement was the incorporation of a land use change (LUC) scheme into the GENIE Earth system model. Using output from a 671-member ensemble of transient GENIE simulations, we build an emulator of the change in atmospheric CO₂ concentration change since the preindustrial period. We use this emulator to sample the 28-dimensional input parameter space. A Bayesian calibration of the emulator output suggests that the increase in gross primary productivity (GPP) in response to a doubling of CO₂ from preindustrial values is very likely (90% confidence) to exceed 20%, with a most likely value of 40–60%. It is important to note that we do not represent all of the possible contributing mechanisms to the terrestrial sink. The missing processes are subsumed into our calibration of CO₂ fertilisation, which therefore represents the combined effect of CO₂ fertilisation and additional missing processes. If the missing processes are a net sink then our estimate represents an upper bound. We derive calibrated estimates of carbon fluxes that are consistent with existing estimates. The present-day land–atmosphere flux (1990–2000) is estimated at −0.7 GTC yr⁻¹ (likely, 66% confidence, in the range 0.4 to −1.7 GTC yr⁻¹). The present-day ocean–atmosphere flux (1990–2000) is estimated to be −2.3 GTC yr⁻¹ (likely in the range −1.8 to −2.7 GTC yr⁻¹). We estimate cumulative net land emissions over the post-industrial period (land use change emissions net of the CO₂ fertilisation and climate sinks) to be 66 GTC, likely to lie in the range 0 to 128 GTC.