Gross primary production (GPP) by terrestrial ecosystems is the largest flux in the global carbon cycle, and its continuing increase in response to environmental changes is key to land ecosystems' capacity to offset anthropogenic CO2 emissions. However, the CO2- and climate-sensitivities of GPP vary among models. We applied the 'P model'—a parameter-sparse and extensively tested light use efficiency (LUE) model, driven by CO2, climate and remotely sensed greenness data—at 29 sites with multi-year eddy-covariance flux measurements. Observed (both positive and negative) GPP trends at these sites were predicted, albeit with some bias. Increasing LUE (due to rising atmospheric CO2 concentration) and green vegetation cover were the primary controls of modelled GPP trends across sites. Global GPP simulated by the same model increased by 0.46 ± 0.09 Pg C yr–2 during 1982–2016. This increase falls in the mid-range rate of simulated increase by the TRENDY v8 ensemble of state-of-the-art ecosystem models. The modelled LUE increase during 1900–2013 was 15%, similar to a published estimate based on deuterium isotopomers. Rising CO2 was the largest contributor to the modelled GPP increase. Greening, which may in part be caused by rising CO2, ranked second but dominated the modelled GPP change over large areas, including semi-arid vegetation on all continents. Warming caused a small net reduction in modelled global GPP, but dominated the modelled GPP increase in high northern latitudes. These findings strengthen the evidence that rising LUE due to rising CO2 level and increased green vegetation cover (fAPAR) are the main causes of increasing GPP, and thereby, the terrestrial carbon sink.