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Our work develops the structural mathematical framework of the REGENerative Agriculture (REGENA) Production Function, contributing to the limited global literature of regenerative farming production functions with consistency to the 2nd Law of Thermodynamics and the underlying biophysical processes for ecosystem services’ generation. The accurate structural economic modeling of regenerative farming practices comprises a first vital step for the shift of global agriculture from conventional farming—utilizing petrochemical fertilizers, pesticides and intensive tillage—to regenerative farming—utilizing local agro-ecological capital forms, such as micro-organisms, organic biomasses, no-tillage and resistant varieties. In this context, we empirically test the REGENA structural change patterns with data from eight experimental plots in six Mediterranean countries in Southern Europe and Northern Africa for three crop compositions: (a) with exclusively conventional practices, (b) with exclusively regenerative practices and (c) with mixed conventional and regenerative practices. Finally, we discuss in detail the scientific, institutional, economic and financial engineering challenges for the market uptake of regenerative farming and the contribution of REGENA for the achievement of this goal. In addition, as regenerative farming is knowledge-intensive, we review the vital aspect of Open Innovation (OI) and protected Intellectual Property (IP) business models as essential parts of regenerative farming knowledge-sharing clusters and trading alliances.