A monatomic layer of graphite (MG or graphene) adsorbed on the (111) faces of transition metals Pt, Ir, and Ni, has been employed for controlling the atomic hydrogen adsorption site selectivity and the amount of hydrogen adsorbed upon saturation. The variations in the graphene-metal chemical bonding caused by hydrogenation and the values of saturated hydrogen coverage have been studied by X-ray photoemission and X-ray absorption spectroscopy. The hydrogenation of the graphene/metal systems has also been compared to the hydrogen adsorption on highly oriented pyrolytic graphite under the same experimental conditions. It has been found that graphene adsorption on the transition metal substrates can drastically enhance the hydrogen uptake values. The highest values have been observed for MG/Ir(111), less for MG/Pt(111), even less for MG/Ni and the least for the adsorption on bulk graphite. The high level of H coverage on MG/Ir and MG/Pt has been assigned to the preferential H adsorption on the more bonding patches (pores) of the MG/metal coincidence lattice. This adsorption creates unpaired electrons which contribute to a strengthening of the graphene-metal bonds. In this way, the densest possible graphane-like patches can be formed on MG/Pt and MG/Ir. On the MG/Ni interface the formation of graphane is obstructed by the strong interfacial bonding.