A general mathematical model of characteristic and non-reflecting boundary conditions for a system of partial differential equations governing unified Electro-Magneto-Hydrodynamic (EMHD) flows is developed. The novelty of this work is that it includes effects of linear polarization and magnetization of the media. A formulation using characteristic wave relations at the boundaries is derived for the extended Maxwell’s equations and the extended Navier-Stokes equations so that it can be used to specify inflow and outflow free boundary conditions. The emphasis is on using recent theoretical results on well-posedness of boundary conditions for standard Navier-Stokes and Maxwell’s equations to construct a systematic method for specifying the physical and numerical boundary conditions for electro-magneto-hydrodynamics. The formulation is fully three-dimensional and suitable for direct numerical implementation. The results show strong influence of electric and magnetic fields on fluid flow characteristics.