Microwave photonic receivers are a promising candidate in breaking the bandwidth limitation of traditional radio-frequency (RF) receivers. To further balance the performance superiority with the requirements regarding size, weight, and power consumption (SWaP), the implementation of integrated microwave photonic microsystems has been considered an upgrade path. However, up to now, to the best of our knowledge, chip-scale fully integrated microwave photonic receivers have not been reported due to the limitation of material platforms. In this paper, we report a fully integrated hybrid microwave photonic receiver (FIH-MWPR) obtained by comprising the indium phosphide (InP) laser chip and the monolithic silicon-on-insulator (SOI) photonic circuit into the same substrate based on the low-coupling-loss micro-optics method. Benefiting from the integration of all optoelectronic components, the packaged FIH-MWPR exhibits a compact volume of $6{\mathrm{cm}}^3$ and low power consumption of 1.2 W. The FIH-MWPR supports a wide operation bandwidth from 2 to 18 GHz. Furthermore, its RF-link performance to down-convert the RF signals to the intermediate frequency is experimentally characterized by measuring the link gain, the noise figure, and the spurious-free dynamic range metrics across the whole operation frequency band. Moreover, we have utilized it as a de-chirp receiver to process the broadband linear frequency-modulated (LFM) radar echo signals at different frequency bands (S-, C-, X-, and Ku-bands) and successfully demonstrated its high-resolution-ranging capability. To the best of our knowledge, this is the first realization of a chip-scale broadband fully integrated microwave photonic receiver, which is expected to be an important step in demonstrating the feasibility of all-integrated microwave photonic microsystems oriented to miniaturized application scenarios.