The transition of a business to a circular business model (CBM) calls for significant and ongoing shifts in different business management models and strategies. However, there is a lack of research focused on the technological, financial, societal, and institutional influences on the CBM transition in small and/or medium-sized enterprises (SMEs). To address this gap, our study develops a theoretical framework for the transition towards CBM. We conducted a systematic literature review with the objective of determining the relationships among technological, financial, societal, and institutional influences for CBMs. Following this, we then established a conceptual framework that comprises these four key influences for a transition plan in the context of an innovative business model with a focus on the value proposition, value creation, and value delivery. An illustrative case example of the manufacturing industry for the transition plan to CBM was presented as well. The proposed framework is designed to lead the shift towards circular economy-oriented business models that aim to promote sustainability in business. In addition, we uncovered several potential avenues for further investigation. We expect the framework towards both contribute to the expansion of the existing body of research in the field and provide business practitioners with guidelines on the CBMs’ transition for SMEs.