Although aligning business models with enterprise architecture concepts can provide insights into business model implementation aspects, current approaches that facilitate business model enterprise architecture have several limitations: they often lack a network perspective, facilitate one level analysis of the business model implementation, are heavyweight or have an informal approach. Therefore, this research presents a formal representation for business model – enterprise architecture alignment, which is developed though an iterative design process with researchers and practitioners. Findings of this study have resulted in a formal business metamodel, a formal business model – enterprise architecture metamodel, two target metamodels and a corresponding modelling procedure. These metamodels facilitate a multi-level description, visualization and analysis of the technological implementation of business models through enterprise architecture concepts. The metamodels are subsequently applied to the Industry 4.0 domain. Main contributions of this study are the formal approach, the development of an intermediate lightweight metamodel to bridge the gap between business models and enterprise architectures, and the proposal of various extensions to enterprise architecture modelling language ArchiMate. Lastly, this study also provides some first insights into Industry 4.0 business model implementation aspects. Further research could focus on the inclusion of a quantitative financial analysis in the business model implementation approach.