We show with angle-resolved photoemission spectroscopy that a new energy band appears in the electronic structure of electron-doped hydrogenated monolayer graphene (H-graphene). Its occupation can be controlled with the hydrogen amount and allows for tuning of graphene's doping level. Our calculations of the electronic structure of H-graphene suggest that this state is largely composed of hydrogen 1s orbitals and remains extended for low H coverages despite the random chemisorption of H. Further evidence for the existence of a hydrogen state is provided by x-ray absorption studies of undoped H-graphene which are clearly showing the emergence of an additional state in the vicinity of the pi* resonance.