The ability to achieve strong-coupling has made cavity-magnon systems an exciting platform for the development of hybrid quantum systems and the investigation of fundamental problems in physics. Unfortunately, current experimental realizations are constrained to operate at a single frequency, defined by the geometry of the microwave cavity. In this article we realize a highly-tunable, cryogenic, microwave cavity strongly coupled to magnetic spins. The cavity can be tuned in situ by up to 1.5 GHz, approximately 15% of its original 10 GHz resonance frequency. Moreover, this system remains within the strong-coupling regime at all frequencies with a cooperativity of ≈ 800.