In cold atomic gases the interactions between the atoms are directly controllable through external magnetic fields. The magnetic field control is typically performed indirectly by stabilizing the current through a pair of Helmholtz coils, which produce this large bias field. Here, we overcome the limitations of such an indirect control through a direct feedback scheme, which is based on nitrogen-vacancy centers acting as a magnetic field sensor. This allows us to measure and stabilize fields of 4.66 mT down to 12 nT RMS noise over the course of 24 h, measured on a 1 Hz bandwidth. We achieve a control of better than 1 ppm after 20 minutes of integration time, ensuring high long-term stability for experiments. This approach extends direct magnetic field control to strong magnetic fields, which could enable new precise quantum simulations in this regime.