The KM3NeT research infrastructure being built at the bottom of the Mediterranean Sea will host water-Cherenkov telescopes for the detection of cosmic neutrinos. The neutrino telescopes will consist of large volume three-dimensional grids of optical modules to detect the Cherenkov light from charged particles produced by neutrino-induced interactions. Each optical module houses 31 3-in. photomultiplier tubes, instrumentation for calibration of the photomultiplier signal and positioning of the optical module, and all associated electronics boards. By design, the total electrical power consumption of an optical module has been capped at seven Watts. We present an overview of the front-end and readout electronics system inside the optical module, which has been designed for a 1-ns synchronization between the clocks of all optical modules in the grid during a life time of at least 20 years.