Drug discovery is a critical task in biomedical natural language processing (NLP), yet explainable drug discovery remains underexplored. Meanwhile, large language models (LLMs) have shown remarkable abilities in natural language understanding and generation. Leveraging LLMs for explainable drug discovery has the potential to improve downstream tasks and real-world applications. In this study, we utilize open-source drug knowledge graphs, clinical trial data, and PubMed publications to construct a comprehensive dataset for the explainable drug discovery task, named \textbf{expRxRec}. Furthermore, we introduce \textbf{KEDRec-LM}, an instruction-tuned LLM which distills knowledge from rich medical knowledge corpus for drug recommendation and rationale generation. To encourage further research in this area, we will publicly release\footnote{A copy is attached with this submission} both the dataset and KEDRec-LM.