Power electronic converter will be a key enabler for future electrified aircraft propulsion system. In aircraft applications, superconducting technologies such as superconducting motors and generators along with supporting power systems will grow in importance. Utilizing cryogenic cooling for power converter potentially can significantly improve the inverter system efficiency and specific power. This paper presents the cooling, hardware, and testing of a cryogenically-cooled MW inverter developed for electrified aircraft propulsion system. The 1 MVA full load testing with cryogenic cooling is demonstrated. The developed inverter system achieves 18 kVA/kg specific power and 99% efficiency, which provides a promising solution to achieve high power density and efficiency for future electrified aircraft propulsion system.