The increasing demand for reliable, rapid, and sustainable last-mile medical deliveries has accelerated the adoption of unmanned aerial vehicle (UAV) technologies. This study proposes a solar-powered UAV system architecture that integrates Global Information Grid (GIG) network layers and cold-chain logistics for the safe transportation of blood, vaccines, biologics, and emergency medication. The architecture combines tiered UAV fleets, a hybrid solar-battery propulsion system, advanced communications, and cloud-based Zero-Trust integration for secure and traceable deliveries. A power-sizing model is presented, showing how solar energy harvest can support autonomous operations with minimal downtime, achieving over 95% operational availability. These results demonstrate the potential of renewable energy UAVs to enhance global health logistics and align with BVLOS operations, WHO PQS standards, and international safety guidelines, with future work exploring scalability and deployment in diverse environments.