The number of baryons hosted in the disks of galaxies (stars and interstellar gas and dust) is lower than expected based on the mass of their dark-matter halos and the fraction of baryon-to-total matter in the universe, giving rise to the so called galaxy missing-baryon problem. The presence of cool circum-galactic matter gravitationally bound to the galaxy up to distances of at least ten times the size of the galaxy’s disk, mitigates the problem but is far from being sufficient for its solution. It has instead been suggested that the galaxy missing baryon may hide in a much hotter gaseous phase of the circum-galactic medium, possibly at the halo virial temperature and co-existing with the cool phase. However, current mass estimates of this possible hot phase are only loose lower limits. Here we exploit the best available X-ray spectroscopic data of known cool circum-galactic systems to show that the galaxy missing baryonic mass is indeed found in a hot medium surrounding the disks of galaxies and permeating their entire halos, at temperatures consistent with their virial temperatures. Main tracers of this hot medium are highly ionized light elements that only retain one or two electrons and that are only visible in the X-rays. Our measurements solve the long-standing galaxy missing baryon problems and contribute importantly to the understanding of the continuous cycle of baryons in-and-out of galaxies throughout the life of the universe.