An exact asymptotically flat 3-parameter solution of the Einstein-Maxwell equations is presented that reduces to the Bonnor magnetic dipole solution in the magnetostatic limit, and to the Tomimatsu-Sato = 2 solution in the stationary pure vacuum limit. This solution is the simplest possible one admitting the polynomial representation in the spheroidal coordinates (x, y) and able to describe the exterior field of a magnetized spinning mass. A multipole criterion for the choice of the parameters in the Einstein-Maxwell spacetimes is also formulated.