Hybrid Graphene/magnetic structures offer a unique playground for fundamental research, and opportunities for emerging technologies. Graphene-spaced ultrathin structures with antiferromagnetic exchange-coupling (AFC) seem a relevant scenario, analogous to that of conventional metallic multilayer devices. Unfortunately, the AFC found so far between bulk magnetic single crystals and Graphene-spaced adatoms, clusters or molecules either requires low temperatures, is too weak, or of complex nature, for realistic exploitation. Here we show theoretically and experimentally that a strong perpendicular AFC can be established in ultrahin-film structures such as Fe/Gr/Co on Ir(111), first-time enabling Graphene-based synthetic antiferromagnet and ferrimagnet materials with unprecedented magnetic properties and appearing suitable for applications. Remarkably, the established AFC is robust on structure thicknesses, thermally stable up to room temperature, very strong but field-controllable, and occurs in perpendicular orientation with opposite high remanent layer magnetizations. Our atomistic first-principle simulations provide further ground for the feasibility of Graphene-mediated AFC ultra-thin film structures, revealing that Graphene acts not only as mere spacer but has a direct role in sustaining antiferromagnetic superexchange-coupling between the magnetic layers. These results provide a path for the design of unique and ultimately-thin synthetic antiferromagnetic structures, which seem exciting for fundamental nanoscience studies or for potential use in Graphene-spintronics applications.