Primary production is at the base of the marine food web and plays a central role for global biogeochemical cycles. Yet global ocean primary production is known to only a factor of ~2, with previous estimates ranging from 38 to 65 Pg C yr−1 and no formal uncertainty analysis. Here, we present an improved global ocean biogeochemistry model that includes a mechanistic representation of photosynthesis and a new observational database of net primary production (NPP) in the ocean. We combine the model and observations to constrain particulate NPP in the ocean with statistical metrics. The PlankTOM5.3 model includes a new photosynthesis formulation with a dynamic representation of iron-light colimitation, which leads to a considerable improvement of the interannual variability of surface chlorophyll. The database includes a consistent set of 50,050 measurements of 14C primary production. The model best reproduces observations when global NPP is 58 ± 7 Pg C yr−1, with a most probable value of 56 Pg C yr−1. The most probable value is robust to the model used. The uncertainty represents 95% confidence intervals. It considers all random errors in the model and observations, but not potential biases in the observations. We show that tropical regions (23°S–23°N) contribute half of the global NPP, while NPPs in the Northern and Southern Hemispheres are approximately equal in spite of the larger ocean area in the South.