Companies around the world are finding themselves in a race against the relentless evolution of digital technologies that are accelerating innovation and creating a highly competitive environment. Many works in research and practice are trying to guide companies to a Digital Transformation (DT) that allows them to take full advantage of new technologies. However, generic solutions, that are mainly focused on technological aspects, make it clear that there is a lack of understanding of the whole scope of their implications. In this sense, this work takes a step back to analyze the origin of the shortcomings of current solution approaches. The results point out a lack of theoretical foundation on identifying the business dimensions implicated in a DT that define its scope. In this sense, this study contributes with a more comprehensive view of the DT process by using a formal approach to define the business dimensions involved in such a change based on the principles of the Socio-Technical Systems (STS) theory. As a result, this proposal goes beyond the purely technological views to (1) identify five business dimensions involved in the DT process: technology, processes, structure, competencies and culture and (2) recognize the key role of strategy and performance measurement, not as dimensions but as external elements that drive and control the DT process. A multiple case study of the DT process of three French manufacturers is presented to validate the proposition. General remarks and future research concerning the implementation of these dimensions conclude this study. CCS CONCEPTS • Applied computing~Enterprise computing~Business-IT alignment • Social and professional topics~Professional topics~Computing and business~Socio-technical systems • Applied computing~Operations research~Industry and manufacturing