The adsorption of atomic H above the carbon buffer layer in the graphene/SiC(0001) interface system is investigated within density functional theory through a set of realistic interface models that do not impose large artificial strains on the graphene. We find that hydrogen binding energies above the buffer layer are two to four times higher than on free-standing graphene and display important spatial variations across the unit cell. Adsorption on Si-bonded, fourfold-coordinated C atoms is strongly unfavorable (unstable, or metastable with very low barriers), while all threefold-coordinated C sites lead to stable configurations often showing H binding energies larger than in H-2. We identify the origin of these large binding energies in the local strengthening of the graphene/SiC interface bonding around the adsorption site due to the H-induced deformation of the graphene buffer layer. The most stable adsorption sites are those having two or three C nearest neighbors (almost) atop the underlying surface Si atoms, because the presence of the adsorbed H atom favors the formation of a local sp(3) arrangement of the graphene. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim