Hospital accreditation has been transferred from high-income countries (HICs) to many low- and middle-income countries (LMICs), supported by a variety of advocates and donor agencies. This review uses a policy transfer theoretical framework to present a structured analysis of the development of hospital accreditation in LMICs. The framework is used to identify how governments in LMICs adopted accreditation from other settings and what mechanisms facilitated and hindered the transfer of accreditation. The review examines the interaction between national and international actors, and how international organizations influenced accreditation policy transfer. Relevant literature was found by searching databases and selected websites; 78 articles were included in the analysis process. The review concludes that accreditation is increasingly used as a tool to improve the quality of healthcare in LMICs. Many countries have established national hospital accreditation programmes and adapted them to fit their national contexts. However, the implementation and sustainability of these programmes are major challenges if resources are scarce. International actors have a substantial influence on the development of accreditation in LMICs, as sources of expertise and pump-priming funding. There is a need to provide a roadmap for the successful development and implementation of accreditation programmes in low-resource settings. Analysing accreditation policy processes could provide contextually sensitive lessons for LMICs seeking to develop and sustain their national accreditation programmes and for international organizations to exploit their role in supporting the development of accreditation in LMICs.