This work demonstrates a design approach which enables the fabrication of fully integrated radio frequency (RF) and millimetre-wave frequency direct-conversion graphene receivers by adapting the frontend architecture to exploit the state-of-the-art performance of the recently reported wafer-scale CVD metal-insulator-graphene (MIG) diodes. As a proof-of-concept, we built a fully integrated microwave receiver in the frequency range 2.1-2.7 GHz employing the strong nonlinearity and the high responsivity of MIG diodes to successfully receive and demodulate complex, digitally modulated communication signals at 2.45 GHz. In addition, the fabricated receiver uses zero-biased MIG diodes and consumes zero dc power. With the flexibility to be fabricated on different substrates, the prototype receiver frontend is fabricated on a low-cost, glass substrate utilising a custom-developed MMIC process backend which enables the high performance of passive components. The measured performance of the prototype makes it suitable for Internet-of-Things (IoT) and Radio Frequency Identification (RFID) systems for medical and communication applications.