The transfer of graphene grown by chemical vapor deposition (CVD) using amorphous polymers represents a widely implemented method for graphene-based electronic device fabrication. However, the most commonly used polymer, poly(methyl methacrylate) (PMMA), leaves a residue on the graphene that limits the mobility. Here we report a method for graphene transfer and patterning that employs a perfluoropolymer—Hyflon—as a transfer handle and to protect the graphene against contamination from photoresists or other polymers. CVD-grown graphene transferred this way onto LaAlO3/SrTiO3 heterostructures is atomically clean, with high mobility (˜30,000 cm-2V−1s−1) near the Dirac point at 2 K and clear, quantized Hall and magnetoresistance. Local control of the LaAlO3/SrTiO3 interfacial metal-insulator transition—through the graphene—is preserved with this transfer method. The use of perfluoropolymers, such as Hyflon, with CVD-grown graphene and other 2D materials can readily be implemented with other polymers or photoresists.