Silicon photonics enables wafer-scale integration of optical functionalities on chip. Silicon-based laser frequency combs can provide integrated sources of mutually coherent laser lines for terabit-per-second transceivers, parallel coherent light detection and ranging, or photonics-assisted signal processing. We report heterogeneously integrated laser soliton microcombs combining both indium phospide/silicon (InP/Si) semiconductor lasers and ultralow-loss silicon nitride (Si3N4) microresonators on a monolithic silicon substrate. Thousands of devices can be produced from a single wafer by using complementary metal-oxide-semiconductor-compatible techniques. With on-chip electrical control of the laser-microresonator relative optical phase, these devices can output single-soliton microcombs with a 100-gigahertz repetition rate. Furthermore, we observe laser frequency noise reduction due to self-injection locking of the InP/Si laser to the Si3N4 microresonator. Our approach provides a route for large-volume, low-cost manufacturing of narrow-linewidth, chip-based frequency combs for next-generation high-capacity transceivers, data centers, space and mobile platforms.