This study developed a multi-agent system based on Large Language Models (LLMs) to optimize the design process of endogenous educational games. The research was conducted using Design Science Research methodology, following the stages of problem awareness, artifact proposition, development, evaluation, and communication of results. The system integrates four specialized functional modules: AI-assisted Brainstorming, Socratic Agent for conceptual refinement, assisted completion of Endo-GDC (Game Design Canvas for Endogenous Educational Games), and educational objectives classification based on Bloom's Revised Taxonomy. Twenty-six case studies were analyzed spanning different educational contexts, from elementary education to corporate training, encompassing subjects such as mathematics, sciences, languages. Agents were categorized into four types: Coordinator, Mechanics Specialist, Narrative Specialist, and Engagement Specialist. Results evidenced high technological acceptance, with perceived usefulness of 6.23 on a 7-point scale, task-technology fit of 5.95, satisfactory algorithmic experience of 5.80, and processual effectiveness of 5.89. As part of validation, four established frameworks (TAM, TTF, AX, and ADDIE) were applied, confirming system effectiveness in reducing development time while maintaining pedagogical quality. It was concluded that the LLM-based multi-agent approach represents a robust tool for democratizing access to educational game design, showing promise for accelerating pedagogical innovation and expanding the use of active methodologies in education.