The Magellanic Stream is one of the most complex gaseous structures in the Milky Way’s immediate environment. The Large and Small Magellanic Clouds (LMC/SMC), through their mutual interactions over the past several billion years, have lost over a billion solar masses through tidal and ram pressure forces, and the Milky Way has stretched this gas into the Magellanic Stream we see today. It is a massive, multi-phase, filamentary, turbulent structure that we are only now beginning to fully understand. Recent work using absorption line spectroscopy along quasar sightlines has revealed a huge amount of ionized gas that cocoons the directly observable neutral hydrogen first mapped in 1974. This ionized component of the Stream contributes ~90% of the total mass, and until now there hasn’t been an explanation for the source of this majority of the Stream in tidal models. Here we present novel N-body hydrodynamical simulations of the tidal and ram pressure interactions between the LMC, SMC, and Milky Way that lead to the formation of the Magellanic Stream and Leading Arm. We include, for the first time, a Magellanic Corona of warm, ionized gas surrounding the Magellanic Clouds throughout their interactions that can account for the currently observed mass and multi-phase nature of the Stream. This Magellanic Corona is well motivated by the discovery of dwarf galaxies associated with the Magellanic Group, the high mass of the LMC (~2×1011 solar masses), and the warm circumgalactic gas found around LMC-like galaxies in cosmological simulations. We predict that this Magellanic Corona will be unambiguously observable via high-ionization absorption lines in the ultraviolet spectra of background quasars lying near the LMC. This prediction is directly testable with the Cosmic Origins Spectrograph on the Hubble Space Telescope.