Lattices of Ir clusters have been grown by vapor phase deposition on graphene moirés on Ir(111). The clusters are highly ordered, spatially and thermally stable below 500K. Their narrow size distribution is tunable from 4 to about 130 atoms. A model for cluster binding to the graphene is presented based on scanning tunneling microscopy and density functional theory. The proposed binding mechanism suggests that similar cluster lattices might be grown of materials other than Ir.