Satellite remote sensing has been widely used in the last decades for agricultural applications, {both for assessing vegetation condition and for subsequent yield prediction.} Existing remote sensing-based methods to estimate gross primary productivity (GPP), which is an important variable to indicate crop photosynthetic function and stress, typically rely on empirical or semi-empirical approaches, which tend to over-simplify photosynthetic mechanisms. In this work, we take advantage of all parallel developments in mechanistic photosynthesis modeling and satellite data availability for advanced monitoring of crop productivity. In particular, we combine process-based modeling with the soil-canopy energy balance radiative transfer model (SCOPE) with Sentinel-2 {and Landsat 8} optical remote sensing data and machine learning methods in order to estimate crop GPP. Our model successfully estimates GPP across a variety of C3 crop types and environmental conditions even though it does not use any local information from the corresponding sites. This highlights its potential to map crop productivity from new satellite sensors at a global scale with the help of current Earth observation cloud computing platforms.