Photosynthesis-irradiance and photosynthesis-depth experiments are two standard ways of experimentally quantifying primary production. These measurements have historically formed the backbone for the formulation of mathematical models of primary production and to this day remain an invaluable resource for model development and refinement. From such experiments information on photosynthesis parameters can be extracted, which allows for the quantification of the photosynthesis light dependence, essential in the calculation of primary production. To this day, this is the only avenue for photosynthesis parameters estimation, making such data invaluable for primary production modelling. In the literature, there have been several efforts to form global datasets of photosynthesis parameters, collected at various sites across the world oceans and seas. Here, we use a publicly available global dataset of in situ primary production profiles and construct a new database of photosynthesis parameters. We use an inverse modelling approach that is described in great details, along with the data requirements. For a forward model, we employ a fully solvable analytical model of the production profile, and we use the inverse model to compare it with the measured production profile, while constraining it with measured daily watercolumn production. Using this approach, we successfully recovered 4160 photosynthesis-irradiance parameters from the global oceans, which enabled a model versus data comparison for watercolumn production. The spatio-temporal distribution of the new dataset is presented and compared to existing datasets. Finally, the new photosynthesis parameters dataset is provided publicly, along with metadata needed for the implementation in primary production models.