This paper presents ASTREA, the first agent system to run on flight-certified hardware (TRL 9) for autonomous spacecraft operations, and demonstrates on-orbit operations on the International Space Station (ISS). Using thermal control as a representative use case, we integrate a resource-constrained Large Language Model (LLM) agent with a reinforcement learning controller in an asynchronous architecture tailored to the space-certified platform. Ground experiments demonstrate that LLM-based supervision improves thermal stability and reduces violations, demonstrating the potential of combining semantic reasoning and adaptive control under hardware constraints. ISS on-orbit validation initially struggled with inference latency that was inconsistent with the rapid thermal cycle of a Low Earth Orbit (LEO) satellite. However, by synchronizing with the orbit length, we successfully surpassed baselines, achieving fewer violations, longer episode durations, and improved CPU utilization.