Digital transformation (DT) requires organizations to navigate complex technological and organizational changes, often under conditions of uncertainty. While agile methodologies are widely adopted to address the iterative and cross-functional nature of DT, limited attention has been paid to identifying critical success factors (CSFs) from a socio-technical systems (STS) perspective. This study addresses that gap by integrating and prioritizing CSFs as interdependent elements within a layered socio-technical framework. Drawing on a systematic review of 17 empirical and conceptual studies, we adapt Chow and Cao’s agile success model and validate a set of 14 CSFs across five domains—organizational, people, process, technical, and project—through a Delphi-informed Analytic Hierarchy Process (AHP). The findings reveal that organizational and people-related enablers, particularly management commitment, team capability, and organizational environment, carry the greatest weight in agile-based DT contexts. These results inform a three-layered framework—comprising organizational readiness, agile delivery, and project artefacts—which reflects how social, technical, and procedural factors interact systemically. The study contributes both theoretically, by operationalizing STS theory in the agile DT domain, and practically, by providing a prioritized CSF model to guide strategic planning and resource allocation in transformation initiatives.