Robust monitoring and assessment methods are required to assess circular economy (CE) concepts in terms of their degree of circularity and their contribution to sustainability. This research aimed to develop an integrated framework for the CE context—considering both the technical circularity and the complexity of the three dimensions of sustainability (environment, economy, and social). Two existing methods were identified as an appropriate foundation: CE indicators and life cycle sustainability assessment (LCSA), combining life cycle assessment (LCA), life cycle costing (LCC), and social life cycle assessment (S-LCA). The developed circular life cycle sustainability assessment (C-LCSA) framework added circularity assessment (CA) as an additional dimension to LCSA (C-LCSA = LCA + LCC + S-LCA + CA). The abundance of CE indicators required a systematic selection process to identify the most appropriate indicators for the framework which was built on criteria levels, performance, loops, unit, dimension, and transversality. The material circularity indicator, product circularity indicator, and longevity indicator were identified as most suited for C-LCSA. Being developed for a single life cycle, the traditional life cycle approaches needed refinements for application to CE concepts, derived from discussions and proposed adaptions presented in the academic literature. The cut-off approach was identified as the most suitable end-of-life allocation method for C-LCSA, being in line with the technical system boundaries. C-LCSA can be used by LCA practitioners to identify trade-offs between an improved circularity and resulting impacts on the environmental, economic, and social pillars to provide a basis for decision making in industrial ecology.