The rise in emergency department (ED) visits globally challenges efficient patient management, especially in clinical triage. Traditionally managed by human professionals, triage is affected by variability and workload. Large language models (LLMs) offer promising reasoning and understanding capabilities, but using them directly in clinical triage is complex due to the need for domain-specific accuracy and the intricate nature of the process. To address these issues, we introduce TriageAgent, a novel heterogeneous multi-agent framework enhancing collaborative decision-making for clinical triage. TriageAgent utilizes LLMs with self-confidence and early-stopping mechanisms in multi-round discussions to improve reasoning and proficiency. It also employs the medical ESI handbook through a retrieval-augmented generation (RAG) approach for precise triage knowledge and integrates both coarse- and fine-grained ESI-level predictions. Extensive experiments show that TriageAgent outperforms state-of-the-art GPT-based methods on three professional clinical datasets. Additionally, we have released the first public benchmark dataset for clinical triage with ESI levels and provided benchmark human expert performance for comparison.