Query and product relevance prediction is a critical component for ensuring a smooth user experience in e-commerce search. Traditional studies mainly focus on BERT-based models to assess the semantic relevance between queries and products. However, the discriminative paradigm and limited knowledge capacity of these approaches restrict their ability to comprehend the relevance between queries and products fully. With the rapid advancement of Large Language Models (LLMs), recent research has begun to explore their application to industrial search systems, as LLMs provide extensive world knowledge and flexible optimization for reasoning processes. Nonetheless, directly leveraging LLMs for relevance prediction tasks introduces new challenges, including a high demand for data quality, the necessity for meticulous optimization of reasoning processes, and an optimistic bias that can result in over-recall. To overcome the above problems, this paper proposes a novel framework called the LLM-based RElevance Framework (LREF) aimed at enhancing e-commerce search relevance. The framework comprises three main stages: supervised fine-tuning (SFT) with Data Selection, Multiple Chain of Thought (Multi-CoT) tuning, and Direct Preference Optimization (DPO) for de-biasing. We evaluate the performance of the framework through a series of offline experiments on large-scale real-world datasets, as well as online A/B testing. The results indicate significant improvements in both offline and online metrics. Ultimately, the model was deployed in a well-known e-commerce application, yielding substantial commercial benefits.