We show by angle-resolved photoemission spectroscopy that a tunable gap in quasi-free-standing monolayer graphene on Au can be induced by hydrogenation. The size of the gap can be controlled via hydrogen loading and reaches approximately 1.0 eV for a hydrogen coverage of 8%. The local rehybridization from sp(2) to sp(3) in the chemical bonding is observed by X-ray photoelectron spectroscopy and X-ray absorption and allows for a determination of the amount of chemisorbed hydrogen. The hydrogen induced gap formation is completely reversible by annealing without damaging the graphene. Calculations of the hydrogen loading dependent core level binding energies and the spectral function of graphene are in excellent agreement with photoemission experiments. Hydrogenation of graphene gives access to tunable electronic and optical properties and thereby provides a model system to study hydrogen storage in carbon materials.