Integrated circuits based on complementary metal-oxide-semiconductors (CMOS) are at the heart of the technological revolution of the past 40 years, enabling compact and low-cost microelectronic circuits and imaging systems. However, the diversification of this platform into applications other than microcircuits and visible-light cameras has been impeded by the difficulty to combine semiconductors other than silicon with CMOS. Here, we report the monolithic integration of a CMOS integrated circuit with graphene, operating as a high-mobility phototransistor. We demonstrate a high-resolution, broadband image sensor and operate it as a digital camera that is sensitive to ultraviolet, visible and infrared light (300-2,000 nm). The demonstrated graphene-CMOS integration is pivotal for incorporating 2D materials into the next-generation microelectronics, sensor arrays, low-power integrated photonics and CMOS imaging systems covering visible, infrared and terahertz frequencies.