Vertical heterojunction NiO/β n-Ga₂O/n⁺ Ga₂O₃ rectifiers employing NiO layer extension beyond the rectifying contact for edge termination exhibit breakdown voltages (V_B) up to 4.7 kV with a power figure-of-merits, V_B²/R_ON of 2 GW·cm⁻², where R_ON is the on-state resistance (11.3 mΩ cm²). Conventional rectifiers fabricated on the same wafers without NiO showed V_B values of 840 V and a power figure-of-merit of 0.11 GW cm⁻². Optimization of the design of the two-layer NiO doping and thickness and also the extension beyond the rectifying contact by TCAD showed that the peak electric field at the edge of the rectifying contact could be significantly reduced. The leakage current density before breakdown was 144 mA/cm², the forward current density was 0.8 kA/cm² at 12 V, and the turn-on voltage was in the range of 2.2–2.4 V compared to 0.8 V without NiO. Transmission electron microscopy showed sharp interfaces between NiO and epitaxial Ga₂O₃ and a small amount of disorder from the sputtering process.