Two-dimensional hexagonal arrays of Pt nanoparticles (1.5 nm diameter) have been obtained by deposition of preformed and size selected Pt nanoparticles on graphene. This original self-organization is induced, at room temperature, by the 2D periodic undulation (the moiré pattern) of graphene epitaxially grown on the Ir(111) surface. By means of complementary techniques (scanning tunneling microscopy, grazing incidence X ray scattering), the Pt clusters shapes and organization are characterized and the structural evolution during annealing is investigated. The soft-landed clusters remain quasi-spherical and a large proportion appears to be pinned on specific moiré sites. The quantitative determination of the proportion of organized clusters reveals that the obtained hexagonal array of the almost spherical nanoparticles is stable up to 650 K, which is an indication of a strong cluster-surface interaction.