The purpose of this paper is to examine whether it is possible to define a conceptual framework for measuring the success of digital transformation projects, which will comprehensively and integrally respond to the complexity of this undertaking. In accordance with that, a review of the literature on the concept of project success was carried out, with a special emphasis on the success and critical success factors of software projects. Based on the methodological criteria obtained in the literature review, the concept and characteristics of digital transformation projects were analyzed. The key results obtained in this work are the multidimensional concept of success, which consists of three dimensions, software project success, digital transformation success, strategic digital transformation success, as well as identified groups of critical success factors for each of the success dimensions. In addition to the identification and grouping of critical success factors within the success dimensions, a hierarchy of success levels was identified from the success of software part of project to the strategic success. Based on the proposed conceptual model, future research directions are defined, which include the development of a balanced set of performance measures for each group of critical success factors and the implementation of empirical research. The results of this work can serve the scientific community, but also people in practice to critically look at current attitudes and practices in this area.