Legal Passage Retrieval (LPR) systems are crucial as they help practitioners save time when drafting legal arguments. However, it remains an underexplored avenue. One primary reason is the significant vocabulary mismatch between the query and the target passage. To address this, we propose a simple yet effective method, the $\textbf{G}$enerative q$\textbf{u}$ery $\textbf{RE}$writer $\textbf{(GuRE)}$. We leverage the generative capabilities of Large Language Models (LLMs) by training the LLM for query rewriting. $\textit{"Rewritten queries"}$ help retrievers to retrieve target passages by mitigating vocabulary mismatch. Experimental results show that GuRE significantly improves performance in a retriever-agnostic manner, outperforming all baseline methods. Further analysis reveals that different training objectives lead to distinct retrieval behaviors, making GuRE more suitable than direct retriever fine-tuning for real-world applications. Codes are avaiable at github.com/daehuikim/GuRE.