The covalent functionalization of graphene with long-range periodicity is highly desirable to provide control over its electronic, optical, or magnetic properties. We describe a method for the site-selective, covalent modification of graphene with strict spatial periodicity at the nanometer scale. The periodic landscape is provided by a single monolayer of graphene epitaxially grown on Ru(0001), that presents a moiré pattern with 3 nm periodicity due to the mismatch between the carbon and ruthenium hexagonal lattices. The moiré contains periodically arranged sites where the charge transfer from the metallic substrate is enhanced as a result of the local graphene-ruthenium interaction and, as a consequence, these sites show higher chemical reactivity. This is illustrated by imaging with STM under UHV conditions the attachment of cyanomethyl radicals (CH₂CN^) produced by homolytic breaking of acetonitrile (CH₃CN), which present an almost ideal (98%) site selectivity to bind covalently to graphene on these areas. The subsequent specific reaction of the cyanomethyl radicals with TCNQ is observed in the real space by STM and STS, which reveals the specific character of the bond formed.