We present a current-monitoring system based on optical magnetometry, which is able to discriminate true current variations from environmental effects at room temperature. The system consists of a dedicated thermally stable magnetic-field-confining coil and an array of four optically pumped magnetometers arranged in a two-dimensional gradiometer configuration. These magnetometers monitor magnetic field variations inside the coil, which correlate with the variations of the driving current of the coil. The system uses a digital signal-processing unit to extract and record in real time the magnetic field values measured by the magnetometers, which allows real-time monitoring of the current. The coil of the system, which is made out of printed circuit boards, can easily be changed to adapt the current-to-field conversion. Thus, we can expand the applicability of this system to a wide range of currents. By using this system to actively feedback control a current source, we stabilize a current of 20 mA on a level better than 5 × 10^-9 for an integration time of 70 min.