Recently, researchers have investigated the capabilities of Large Language Models (LLMs) for generative recommender systems. Existing LLM-based recommender models are trained by adding user and item IDs to a discrete prompt template. However, the disconnect between IDs and natural language makes it difficult for the LLM to learn the relationship between users. To address this issue, we propose a PErsonAlized PrOmpt Distillation (PeaPOD) approach, to distill user preferences as personalized soft prompts. Considering the complexities of user preferences in the real world, we maintain a shared set of learnable prompts that are dynamically weighted based on the user's interests to construct the user-personalized prompt in a compositional manner. Experimental results on three real-world datasets demonstrate the effectiveness of our PeaPOD model on sequential recommendation, top-n recommendation, and explanation generation tasks.