This paper demonstrates the conversion of a ⁸⁷Rb atomic optical frequency standard to a highly stable microwave frequency standard using an integrated optical frequency comb. First, an integrated ⁸⁷Rb atomic optical frequency standard was designed and constructed. The frequency of a 780 nm laser was locked to the 5S_1/2(F=2)-5P_3/2(F’=3) transition of ⁸⁷Rb atoms using modulation transfer spectroscopy. The stabilized laser achieved a frequency stability of 9.9×10^-14 at 1 s and a linewidth of approximately 37.1 kHz. On this basis, the carrier-envelope offset frequency f_ceo and repetition frequency f_r of the integrated fiber optical frequency comb were simultaneously referenced to a hydrogen maser, enabling absolute frequency measurement of the ⁸⁷Rb 5S_1/2(F=2)-5P_3/2(F’=3) transition. Furthermore, without relying on a hydrogen maser, the optical frequency comb was locked based on the ⁸⁷Rb atomic optical frequency standard to generate a microwave signal, thereby effectively transferring the optical frequency stability to the microwave domain, with the generated microwave stability consistent with that of the optical frequency standard. At an averaging time of 10 s, the frequency stability of the microwave signal reached 1.6×10^-13. The short-term stability is close to the level of commercial cesium fountain clocks. The optically generated microwave device features a simple structure and a high degree of integration, showing good potential for transportable applications and providing technical support for high-performance microwave frequency references and portable atomic clock systems.