The control of a ferromagnets magnetization via only electric currents requires the efficient generation of current-driven spin-torques. In magnetic structures based on topological insulators (TIs) current-induced spin-orbit torques can be generated. Here we show that the addition of graphene, or bilayer graphene, to a TI-based magnetic structure greatly enhances the current-induced spin density accumulation and significantly reduces the amount of power dissipated. We find that this enhancement can be as high as a factor of 100, giving rise to a giant Edelstein effect. Such a large enhancement is due to the high mobility of graphene (bilayer graphene) and to the fact that the graphene (bilayer graphene) sheet very effectively screens charge impurities, the dominant source of disorder in topological insulators. Our results show that the integration of graphene in spintronics devices can greatly enhance their performance and functionalities.