Earth observation-based estimates of global gross primary production (GPP) are essential for understanding the response of the terrestrial biosphere to climatic change and other anthropogenic forcing. In this study, we attempt an ecosystem-level physiological approach of estimating GPP using an asymptotic light response function (LRF) between GPP and incoming photosynthetically active radiation (PAR) that better represents the response observed at high spatiotemporal resolutions than the conventional light use efficiency approach. Modelled GPP is thereafter constrained with meteorological and hydrological variables. The variability in field-observed GPP, net primary productivity and solar-induced fluorescence was better or equally well captured by our LRF-based GPP when compared with six state-of-the-art Earth observation-based GPP products. Over the period 1982–2015, the LRF-based average annual global terrestrial GPP budget was 121.8 ± 3.5 Pg C, with a detrended inter-annual variability of 0.74 ± 0.13 Pg C. The strongest inter-annual variability was observed in semi-arid regions, but croplands in China and India also showed strong inter-annual variations. The trend in global terrestrial GPP during 1982–2015 was 0.27 ± 0.02 Pg C year⁻¹, and was generally larger in the northern than the southern hemisphere. Most positive GPP trends were seen in areas with croplands whereas negative trends were observed for large non-cropped parts of the tropics. Trends were strong during the eighties and nineties but levelled off around year 2000. Other GPP products either showed no trends or continuous increase throughout the study period. This study benchmarks a first global Earth observation-based model using an asymptotic light response function, improving simulations of GPP, and reveals a stagnation in the global GPP after the year 2000.