The polymer-supported transfer of chemical vapor deposition (CVD)-grown graphene provides large-area and high-quality graphene on a target substrate; however, the polymer and organic solvent residues left by the transfer process hinder the application of CVD-grown graphene in electronic and photonic devices. Here, we describe an inverse transfer method (ITM) that permits the simultaneous transfer and doping of graphene without generating undesirable residues by using polymers with different functional groups. Unlike conventional wet transfer methods, the polymer supporting layer used in the ITM serves as a graphene doping layer placed at the interface between the graphene and the substrate. Polymers bearing functional groups can induce n-doping or p-doping into the graphene depending on the electron-donating or -withdrawing characteristics of functional groups. Theoretical models of dipole layer-induced graphene doping offered insights into the experimentally measured change in the work function and the Dirac point of the graphene. Finally, the electrical properties of pentacene field effect transistors prepared using graphene electrodes could be enhanced by employing the ITM to introduce a polymer layer that tuned the work function of graphene. The versatility of polymer functional groups suggests that the method developed here will provide valuable routes to the development of applications of CVD-grown graphene in organic electronic devices.