Despite its roots in environmental discussions, sustainability has become a critical term influencing every aspect of organisations. As human-oriented institutions, universities have also embraced the 'sustainable development' concept on the quality of their internal and external services. Two overarching questions are most important for university managers to strategically guide sustainable quality development in their institutions: Which strategies do university managers adapt to construct a "sustainable quality management" structure in their universities? and how are these adapted strategies related to different aspects/components of universities? In response, we employed a Systematic Literature Review (SLR) protocol to analyse the existing studies in the related literature. During the systematic review, we followed five steps sequentially: i) defining the research question(s), ii) setting inclusion-exclusion criteria, iii) recording eligible studies, iv) quality overview of selected studies, and v) discussing prominent results. To integrate the results, we benefitted from five enablers in the European Foundation for Quality Management (EFQM) model and the sub-sections given in the European University Association's (EUA) institutional evaluation reports. The results revealed that the initial steps for university leadership to establish a `Sustainable Quality Management' system are integrating a sustainable quality approach to the main strategy document, and then motivating their staff to participate in and enrich the reform-level cultural changes in their universities. This study also discusses the strategies adapted to sustain quality development in universities' teaching, research, societal services, and internationalisation practices.