Synthetic two-dimensional polymorphs of boron, or borophene, have attracted attention because of their anisotropic metallicity, correlated-electron phenomena, and diverse superlattice structures. Although borophene heterostructures have been realized, ordered chemical modification of borophene has not yet been reported. Here, we synthesize "borophane" polymorphs by hydrogenating borophene with atomic hydrogen in ultrahigh vacuum. Through atomic-scale imaging, spectroscopy, and first-principles calculations, the most prevalent borophane polymorph is shown to possess a combination of two-center-two-electron boron-hydrogen and three-center-two-electron boron-hydrogen-boron bonds. Borophane polymorphs are metallic with modified local work functions and can be reversibly returned to pristine borophene through thermal desorption of hydrogen. Hydrogenation also provides chemical passivation because borophane reduces oxidation rates by more than two orders of magnitude after ambient exposure.