Monolithic microwave integrated circuits (MMICs) are an emerging technology that is expected to substantially improve telecommunications in the next few years1,2. MMICs use application-specific semiconductors to meet the performance needs of 5G standards and beyond; however, integrating high-frequency switches into these platforms is very demanding in terms of area and cost and doing so is also a bottleneck for performance3. Memristive radio-frequency switches are an appealing alternative due to their easy fabrication and high device-level electrical performance, but their use in circuit implementations of MMICs has never been realized4. Here we demonstrate programmable millimetre-wave (mmWave) gallium nitride (GaN) MMICs fabricated with memristive radio-frequency switches made from two-dimensional layered hexagonal boron nitride (hBN) integrated directly on the back-end-of-line. We fabricated back-end-of-line wideband switches operating up to 100 GHz with insertion losses as low as 0.3 dB and isolation better than 15 dB. The switches delivered long-term state retention (2 weeks), stable on-state resistance at 175 °C, linear power handling within 0.28 dB measured up to 18 dBm, and an extrapolated 1-dB compression point mean of 30.52 dBm. We use one-transistor, one-memristor cell integration for the switch drivers, achieving 3,250 cycles of endurance, an improvement for two-dimensional-material-based memristive radio-frequency switches. Finally, we demonstrate the implementation of memristive-configurable attenuators, power dividers and programmable resonators on the GaN MMIC platform.