Large-area graphene films are best synthesized via chemical vapour and/or solid deposition methods at elevated temperatures (~1,000 °C) on polycrystalline metal surfaces and later transferred onto other substrates for device applications. Here we report a new method for the synthesis of graphene films directly on SiO(2)/Si substrates, even plastics and glass at close to room temperature (25-160 °C). In contrast to other approaches, where graphene is deposited on top of a metal substrate, our method invokes diffusion of carbon through a diffusion couple made up of carbon-nickel/substrate to form graphene underneath the nickel film at the nickel-substrate interface. The resulting graphene layers exhibit tunable structural and optoelectronic properties by nickel grain boundary engineering and show micrometre-sized grains on SiO(2) surfaces and nanometre-sized grains on plastic and glass surfaces. The ability to synthesize graphene directly on non-conducting substrates at low temperatures opens up new possibilities for the fabrication of multiple nanoelectronic devices.