Microwave photonic technologies, which upshift the carrier into the optical domain to facilitate the generation and processing of ultrawide-band electronic signals at vastly reduced fractional bandwidths, have the potential to achieve superior performance compared to conventional electronics for targeted functions. For microwave photonic applications such as filters, coherent radars, subnoise detection, optical communications and low-noise microwave generation, frequency combs are key building blocks. By virtue of soliton microcombs, frequency combs can now be built using CMOS compatible photonic integrated circuits, operated with low power and noise, and have already been employed in system-level demonstrations. Yet, currently developed photonic integrated microcombs all operate with repetition rates significantly beyond those that conventional electronics can detect and process, compounding their use in microwave photonics. Here we demonstrate integrated soliton microcombs operating in two widely employed microwave bands, X- and K-band. These devices can produce more than 300 comb lines within the 3-dB-bandwidth, and generate microwave signals featuring phase noise levels below 105 dBc/Hz (140 dBc/Hz) at 10 kHz (1 MHz) offset frequency, comparable to modern electronic microwave synthesizers. In addition, the soliton pulse stream can be injection-locked to a microwave signal, enabling actuator-free repetition rate stabilization, tuning and microwave spectral purification, at power levels compatible with silicon-based lasers (<150 mW). Our results establish photonic integrated soliton microcombs as viable integrated low-noise microwave synthesizers. Further, the low repetition rates are critical for future dense WDM channel generation schemes, and can significantly reduce the system complexity of photonic integrated frequency synthesizers and atomic clocks.