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Microwave photonics (MWP), harnessing the tremendous bandwidth of light to generate, process and measure wideband microwave signals, are poised to spark a new revolution for the information and communication fields. Within the past decade, new opportunity for MWP has emerged driven by the advances of integrated photonics. However, despite significant progress made in terms of integration level, a fully on-chip MWP functional system comprising all the necessary photonic and electronic components, is yet to be demonstrated. Here, we break the status quo and provide a complete on-chip solution for MWP system, by exploiting hybrid integration of indium phosphide, silicon photonics and complementary metal-oxide-semiconductor (CMOS) electronics platforms. Applying this hybrid integration methodology, a fully chip-based MWP microwave instantaneous frequency measurement (IFM) system is experimentally demonstrated. The unprecedented integration level brings great promotion to the compactness, reliability, and performances of the overall MWP IFM system, including a wide frequency measurement range (2-34 GHz), ultralow estimation errors (10.85 MHz) and a fast response speed (0.3 ns). Furthermore, we deploy the chip-scale MWP IFM system into realistic application tasks, where diverse microwave signals with rapid-varying frequencies at X-band (8-12 GHz) are accurately identified in real-time. This demonstration marks a milestone for the development of integrated MWP, by providing the technology basis for the miniaturization and massive implementations of various MWP functional systems.