Research increasingly seeks both to generate knowledge and to contribute to real-world solutions, with strong emphasis on context and social engagement. As boundaries between disciplines are crossed, and as research engages more with stakeholders in complex systems, traditional academic definitions and criteria of research quality are no longer sufficient—there is a need for a parallel evolution of principles and criteria to define and evaluate research quality in a transdisciplinary research (TDR) context. We conducted a systematic review to help answer the question: What are appropriate principles and criteria for defining and assessing TDR quality? Articles were selected and reviewed seeking: arguments for or against expanding definitions of research quality, purposes for research quality evaluation, proposed principles of research quality, proposed criteria for research quality assessment, proposed indicators and measures of research quality, and proposed processes for evaluating TDR. We used the information from the review and our own experience in two research organizations that employ TDR approaches to develop a prototype TDR quality assessment framework, organized as an evaluation rubric. We provide an overview of the relevant literature and summarize the main aspects of TDR quality identified there. Four main principles emerge: relevance, including social significance and applicability; credibility, including criteria of integration and reflexivity, added to traditional criteria of scientific rigor; legitimacy, including criteria of inclusion and fair representation of stakeholder interests, and; effectiveness, with criteria that assess actual or potential contributions to problem solving and social change.