Automated Drug Combination Extraction (DCE) from large-scale biomedical literature is crucial for advancing precision medicine and pharmacological research. However, existing relation extraction methods primarily focus on binary interactions and struggle to model variable-length n-ary drug combinations, where complex compatibility logic and distributed evidence need to be considered. To address these limitations, we propose RexDrug, an end-to-end reasoning-enhanced relation extraction framework for n-ary drug combination extraction based on large language models. RexDrug adopts a two-stage training strategy. First, a multi-agent collaborative mechanism is utilized to automatically generate high-quality expert-like reasoning traces for supervised fine-tuning. Second, reinforcement learning with a multi-dimensional reward function specifically tailored for DCE is applied to further refine reasoning quality and extraction accuracy. Extensive experiments on the DrugComb dataset show that RexDrug consistently outperforms state-of-the-art baselines for n-ary extraction. Additional evaluation on the DDI13 corpus confirms its generalizability to binary drugdrug interaction tasks. Human expert assessment and automatic reasoning metrics further indicates that RexDrug produces coherent medical reasoning while accurately identifying complex therapeutic regimens. These results establish RexDrug as a scalable and reliable solution for complex biomedical relation extraction from unstructured text. The source code and data are available at https://github.com/DUTIR-BioNLP/RexDrug