Repurposing approved drugs offers a time-efficient and cost-effective alternative to traditional drug development. However, in silico prediction of repurposing candidates is challenging and requires the effective collaboration of specialists in various fields, including pharmacology, medicine, biology, and bioinformatics. Fragmented, specialized algorithms and tools often address only narrow aspects of the overall problem. Heterogeneous, unstructured data landscapes require the expertise of specialized users. Hence, these data services do not integrate smoothly across workflows. With ChatDRex, we present a conversation-based, multi-agent system that facilitates the execution of complex bioinformatic analyses aiming for network-based drug repurposing prediction. It builds on the integrated systems medicine knowledge graph (NeDRex KG). ChatDRex provides natural language access to its extensive biomedical knowledge base. It integrates bioinformatics agents for network analysis, literature mining, and drug repurposing. These are complemented by agents that evaluate functional coherence for in silico validation. Its flexible multi-agent design assigns specific tasks to specialized agents, including query routing, data retrieval, algorithm execution, and result visualization. A dedicated reasoning module keeps the user in the loop and allows for hallucination detection. By enabling physicians and researchers without computer science expertise to control complex analyses with natural language, ChatDRex democratizes access to bioinformatics as an important resource for drug repurposing. It enables clinical experts to generate hypotheses and explore drug repurposing opportunities, ultimately accelerating the discovery of novel therapies and advancing personalized medicine and translational research. ChatDRex is publicly available at apps.cosy.bio/chatdrex.