Graphene has attracted worldwide interest since its experimental discovery(1,2), but the preparation of large-area, continuous graphene film on SiO2/Si wafers, free from growth-related morphological defects or transfer-induced cracks and folds, remains a formidable challenge(3). Growth of graphene by chemical vapour deposition on Cu foils(4-7) has emerged as a powerful technique owing to its compatibility with industrial-scale roll-to-roll technology(6). However, the polycrystalline nature and microscopic roughness of Cu foils means that such roll-to-roll transferred films are not devoid of cracks and folds(6,7). High-fidelity transfer or direct growth of high-quality graphene films on arbitrary substrates is needed to enable wide-ranging applications in photonics or electronics, which include devices such as optoelectronic modulators, transistors, on-chip biosensors and tunnelling barriers(3,8,9). The direct growth of graphene film on an insulating substrate, such as a SiO2/Si wafer, would be useful for this purpose, but current research efforts remain grounded at the proof-of-concept stage, where only discontinuous, nanometre-sized islands can be obtained(10). Here we develop a face-to-face transfer method for wafer-scale graphene films that is so far the only known way to accomplish both the growth and transfer steps on one wafer. This spontaneous transfer method relies on nascent gas bubbles and capillary bridges between the graphene film and the underlying substrate during etching of the metal catalyst, which is analogous to the method used by tree frogs to remain attached to submerged leaves(11,12). In contrast to the previous wet(4,5,13-15) or dry(6,7) transfer results, the face-to-face transfer does not have to be done by hand and is compatible with any size and shape of substrate; this approach also enjoys the benefit of a much reduced density of transfer defects compared with the conventional transfer method. Most importantly, the direct growth and spontaneous attachment of graphene on the underlying substrate is amenable to batch processing in a semiconductor production line, and thus will speed up the technological application of graphene.