Accurate query-product relevance labeling is indispensable to generate ground truth dataset for search ranking in e-commerce. Traditional approaches for annotating query-product pairs rely on human-based labeling services, which is expensive, time-consuming and prone to errors. In this work, we explore the application of Large Language Models (LLMs) to automate query-product relevance labeling for large-scale e-commerce search. We use several publicly available and proprietary LLMs for this task, and conducted experiments on two open-source datasets and an in-house e-commerce search dataset. Using prompt engineering techniques such as Chain-of-Thought (CoT) prompting, In-context Learning (ICL), and Retrieval Augmented Generation (RAG) with Maximum Marginal Relevance (MMR), we show that LLM's performance has the potential to approach human-level accuracy on this task in a fraction of the time and cost required by human-labelers, thereby suggesting that our approach is more efficient than the conventional methods. We have generated query-product relevance labels using LLMs at scale, and are using them for evaluating improvements to our search algorithms. Our work demonstrates the potential of LLMs to improve query-product relevance thus enhancing e-commerce search user experience. More importantly, this scalable alternative to human-annotation has significant implications for information retrieval domains including search and recommendation systems, where relevance scoring is crucial for optimizing the ranking of products and content to improve customer engagement and other conversion metrics.