We present the ExtraGalactic Cosmic-Ray Propagator (EGCRProp), a fast Monte Carlo code for the propagation of ultra-high energy cosmic rays in the extragalactic medium. The full three-dimensional trajectories of charged nuclei (from protons up to iron) across regions of coherent magnetic fields are calculated up to ultrarelativistic energies. Interactions with the extragalactic background light leading to energy losses can be taken into account. The dynamical evolution of several parameters, like the particle energy, magnetic rigidity, deviation angle, or total distance traveled were obtained and studied. Different methods for integrating the equations of motion can be applied in the simulation, with arbitrary floating-point precision computation. In this work, we present the EGCRProp main features and results.