Purpose: Digital transformation has become a defining priority for university libraries, yet its success depends heavily on the digital competencies of the staff and managers responsible for implementing it. This study aims to identify and rank the dimensions of digital competency among employees and managers of university libraries affiliated with Iran's Ministry of Science, Research and Technology.

Methodology: This research is applied in terms of purpose and descriptive-survey with a quantitative approach in terms of method. The statistical population included managers, librarians, IT experts, and other specialists in the field of digital transformation in academic libraries of Tehran Province. A sample size of 106 people was determined using stratified purposeful sampling and the Krejcie and Morgan table. The data collection instrument was a researcher-made questionnaire. Content validity was confirmed using the Content Validity Ratio (CVR), and reliability was assessed through Cronbach's Alpha (0.93 overall). Seven digital competency indicators were identified through a literature review and ranked using the Fuzzy TOPSIS multi-criteria decision-making technique.

Findings: Librarians' familiarity with new and smart technologies ranked as the most important indicator, followed by managers' competency in digital-transformation management and their ability to plan and lead digital projects. Indicators related to structured training programs and staff participation opportunities in digital-transformation projects ranked lowest, indicating a gap between existing digital skills and the practical involvement of staff in implementation.

Conclusion: Digital transformation in university libraries is a multidimensional process shaped jointly by human, managerial, cultural, and technological factors. Strengthening the digital competencies of both frontline staff and managers — alongside structured training and genuine participation opportunities — is essential for university libraries to move toward a more user-centered, ecosystem-based service model.