<p>Acquiring process knowledge remains a central challenge in business process management, particularly when process discovery approaches rely on manual elicitation and analysis. Following design science research, this paper proposes a theoretically grounded and empirically validated approach to support process knowledge acquisition using Large Language Models (LLMs). The paper outlines three main contributions. First, drawing from knowledge acquisition theory, 19 design requirements are defined for using LLMs in the knowledge acquisition process. Second, these are instantiated in a proposal, named PKAI, which is a novel multi-agent system that operationalizes the stages of preparation, socialization, and externalization in process discovery through specialized LLM-based agents. Third, the study provides empirical evidence of the benefits and limitations of the approach through three evaluation rounds: (i) a demonstration involving business process analysts validating the design requirements and their mapping to the instantiation, (ii) a quasi-experimental study highlighting that process analysts supported by PKAI perform better in designing conceptual models in semantic and pragmatic dimensions, and (iii) a real-world illustrative case study demonstrating the approach's applicability under business complexity and its impact on the knowledge acquisition process. The paper provides the first LLM-based artifact instantiation spanning the whole knowledge acquisition process.</p>