Legal multi-label classification is a critical task for organizing and accessing the vast amount of legal documentation. Despite its importance, it faces challenges such as the complexity of legal language, intricate label dependencies, and significant label imbalance. In this paper, we propose Legal-LLM, a novel approach that leverages the instruction-following capabilities of Large Language Models (LLMs) through fine-tuning. We reframe the multi-label classification task as a structured generation problem, instructing the LLM to directly output the relevant legal categories for a given document. We evaluate our method on two benchmark datasets, POSTURE50K and EURLEX57K, using micro-F1 and macro-F1 scores. Our experimental results demonstrate that Legal-LLM outperforms a range of strong baseline models, including traditional methods and other Transformer-based approaches. Furthermore, ablation studies and human evaluations validate the effectiveness of our approach, particularly in handling label imbalance and generating relevant and accurate legal labels.