The current work reveals the exact nature of the induced interior and exterior coupled-fields of magneto-electro-elastic ellipsoidal inclusions with non-uniform generalized eigenfields, consisting of eigenstrain, eigenelectric, and eigenmagnetic fields. The medium has general rectilinear anisotropic elastic moduli, piezoelectric, piezomagnetic, dielectric, magneto-electric, and magnetic permeability tensors. The non-uniform eigenfields are assumed to be representable as the product of any arbitrary functions whose arguments are the equation of the boundary of the ellipsoidal inclusion with homogeneous polynomials. As a special case, it has been proved that the homogeneous polynomial eigenstrain, eigenelectric, and eigenmagnetic fields simultaneously induce inhomogeneous polynomial strain, electric, magnetic, stress, electric displacement, and magnetic induction fields of the same degree at the interior points of the inclusion. Certain series forms of the eigenfields in cylindrical coordinates are also treated. A special class of impotent eigenstrain, eigenelectric, and eigenmagnetic fields which give rise to vanishing strain, electric, and magnetic fields within the ellipsoidal domain is introduced and proved. Furthermore, the energies pertinent to the magneto-electro-elastic inclusions with arbitrary geometries and eigenfields are formulated. Also, the exact analytical expressions of the magneto-electro-elastic jump conditions of the generalized stress and the gradient of the generalized displacement fields are obtained. A number of theorems, lemmas, and corollaries in connection with the exact nature of the solution are stated and proved for the first time. The presented formulations and theoretical developments are of great value in the determination of the exact induced interior and exterior coupled-fields of anisotropic quantum wire/quantum dot structures as well as anisotropic piezoelectric/piezomagnetic composites.