Recent advances in large language models (LLMs) have enabled new possibilities in simulating complex physiological systems. We introduce Organ-Agents, a multi-agent framework that simulates human physiology via LLM-driven agents. Each Simulator models a specific system (e.g., cardiovascular, renal, immune). Training consists of supervised fine-tuning on system-specific time-series data, followed by reinforcement-guided coordination using dynamic reference selection and error correction. We curated data from 7,134 sepsis patients and 7,895 controls, generating high-resolution trajectories across 9 systems and 125 variables. Organ-Agents achieved high simulation accuracy on 4,509 held-out patients, with per-system MSEs <0.16 and robustness across SOFA-based severity strata. External validation on 22,689 ICU patients from two hospitals showed moderate degradation under distribution shifts with stable simulation. Organ-Agents faithfully reproduces critical multi-system events (e.g., hypotension, hyperlactatemia, hypoxemia) with coherent timing and phase progression. Evaluation by 15 critical care physicians confirmed realism and physiological plausibility (mean Likert ratings 3.9 and 3.7). Organ-Agents also enables counterfactual simulations under alternative sepsis treatment strategies, generating trajectories and APACHE II scores aligned with matched real-world patients. In downstream early warning tasks, classifiers trained on synthetic data showed minimal AUROC drops (<0.04), indicating preserved decision-relevant patterns. These results position Organ-Agents as a credible, interpretable, and generalizable digital twin for precision diagnosis, treatment simulation, and hypothesis testing in critical care.