A crucial consideration when developing and deploying Large Language Models (LLMs) is the human values to which these models are aligned. In the constitutional framework of alignment models are aligned to a set of principles (the constitution) specified in natural language. However, it is unclear how to fairly determine this constitution with widespread stakeholder input. In this work we propose Grounded Constitutional AI (GCAI), a unified framework for generating constitutions of principles that are representative of both users' general expectations toward AI (general principles) and their interaction-time preferences (contextual principles). We extend the Inverse Constitutional AI (ICAI) approach to generate contextual principles from human preference annotation data by leveraging human-provided \textit{reasons} for their preferences. We supplement these contextual principles with general principles surfaced from user statements of \textit{values} regarding AI. We show that a constitution generated by GCAI is preferred by humans over one generated through ICAI both personally, and for widespread use in governing AI behavior. Additionally participants consider the GCAI constitution to be more morally grounded, coherent, and pluralistic.