A high-precision planar digital electromagnetic actuator with two displacement directions and four discrete positions is presented in this paper. The four discrete positions are located at each corner of a square cavity where a mobile permanent magnet moves thanks to Lorentz forces generated when a driving current passes through two orthogonal wires placed below the cavity. Four fixed permanent magnets are placed around the cavity in order to ensure high-precision magnetic holding of the mobile magnet at each discrete position. An analytical model of the actuator is presented and used to characterize its properties (switching time, energy consumption, and displaceable mass). Based on this model, an experimental prototype has been developed and then characterized. Comparisons between experimental and simulated results are carried out and show good agreement. The positioning repeatability errors have also been characterized according to the input signal in order to qualify the digital behavior of this high-precision actuator. Finally, an application of this digital actuator as a linear conveyor is presented and experimentally tested.