Direct growth of graphene films on dielectric substrates (quartz and silica) is reported, by means of remote electron cyclotron resonance plasma assisted chemical vapor deposition r-(ECR-CVD) at low temperature (650°C). Using a two step deposition process- nucleation and growth- by changing the partial pressure of the gas precursors at constant temperature, mostly monolayer continuous films, with grain sizes up to 500 nm are grown, exhibiting transmittance larger than 92% and sheet resistance as low as 900 Ω·sq-1. The grain size and nucleation density of the resulting graphene sheets can be controlled varying the deposition time and pressure. In additon, first-principles DFT-based calculations have been carried out in order to rationalize the oxygen reduction in the quartz surface experimentally observed. This method is easily scalable and avoids damaging and expensive transfer steps of graphene films, improving compatibility with current fabrication technologies.