Enhancing the device performance of single crystal organic field effect transistors (OFETs) requires both optimized engineering of efficient injection of the carriers through the contact and improvement of the dielectric interface for reduction of traps and scattering centers. Since the accumulation and flow of charge carriers in operating organic FETs takes place in the first few layers of the semiconductor next to the dielectric, the mobility can be easily degraded by surface roughness, charge traps, and foreign molecules at the interface. Here, a novel structure for high-performance rubrene OFETs is demonstrated that uses graphene and hexagonal boron nitride (hBN) as the contacting electrodes and gate dielectric layer, respectively. These heterostacked OFETs are fabricated by lithography-free dry-transfer method that allows the transfer of graphene and hBN on top of an organic single crystal, forming atomically sharp interfaces and efficient charge carrier-injection electrodes without damage or contamination. The resulting heterostructured OFETs exhibit both high mobility and low operating gate voltage, opening up new strategy to make high-performance OFETs and great potential for flexible electronics.