Optimizing distributed training strategies for large-scale deep learning models remains a critical challenge in both industry and academia, demanding extensive domain expertise and manual tuning. Existing automated distributed training frameworks are plagued by over-reliance on prior profiling, poor generalization across models/hardware, and scalability constraints stemming from vast search spaces, impeding real-world applicability. To address these challenges, we propose OptiCo, a model-driven multi-agent framework that leverages Large Language Models (LLMs) to enable automatic and explainable distributed training strategy configuration. OptiCo orchestrates a team of reasoning-driven agents, through a shared Global Message Pool facilitating persistent memory and coordination. By employing inception prompting and Chain-Of-Thought (COT) reasoning, agents iteratively refine configurations, detect bottlenecks, analyze failures, and optimize resource utilization. Evaluated across 25+ configurations spanning diverse model architectures, GPU types and scales, OptiCo outperforms expert-designed strategies within 20 iterations, achieving an average performance improvement of 1.84%, with gains ranging from 0.08% to 8.65%. The source codes are avaiable at https://github.com/TangZhe96/OptiCo-public.