Despite recent advancements, most computational methods for molecule optimization are constrained to single- or double-property optimization tasks and suffer from poor scalability and generalizability to novel optimization tasks. Meanwhile, Large Language Models (LLMs) demonstrate remarkable out-of-domain generalizability to novel tasks. To demonstrate LLMs’ potential for molecule optimization, we introduce \mathtt{MuMOInstruct}, the first high-quality instruction-tuning dataset specifically focused on multi-property molecule optimization tasks. Leveraging \mathtt{MuMOInstruct}, we develop \mathtt{GeLLM^3O}s, a series of instruction-tuned LLMs for molecule optimization. Extensive evaluations across 5 in-domain and 5 out-of-domain tasks demonstrate that \mathtt{GeLLM^3O}s consistently outperform state-of-the-art baselines. \mathtt{GeLLM^3O}s also exhibit outstanding zero-shot generalization to unseen tasks, significantly outperforming powerful closed-source LLMs. Such strong generalizability demonstrates the tremendous potential of \mathtt{GeLLM^3O}s as foundational models for molecule optimization, thereby tackling novel optimization tasks without resource-intensive retraining. \mathtt{MuMOInstruct} and code are accessible through https://github.com/ninglab/GeLLMO.