A fully self‐consistent theory of ferromagnetic waveguide accelerators driven by a relativistic electron beam is developed. The theoretical analysis is based on Faraday’s law, which provides a second‐order partial‐differential equation of the azimuthal magnetic field, under the assumption that &mgr;&egr;≫1. Here &mgr; and &egr; are the permeability and dielectric constant of the waveguide material. The azimuthal magnetic field and axial acceleration field are obtained in forms of integral equations for an arbitrary profile of the drive‐beam currentI(t). In the limit when the conductivity &sgr; of the waveguide material is zero, the acceleration mechanism is similar to the typical wake‐field accelerators. In this limit, the acceleration field is proportional to the square root of the parameter &mgr;/&egr; and can be easily more than 200 MV/m for moderate system parameters. On the other hand, for high conductivity limit, the acceleration mechanism is the magnetic field decay, exhibiting that the electromagnetic fields are a decaying function of the time. With appropriate physical parameters, the acceleration gradient of the magnetic field‐decay accelerator is also very large.