-We report the observation of the Inverse Cotton-Mouton Effect (ICME) i.e. a magnetization induced in a medium by non resonant linearly polarized light propagating in the presence of a transverse magnetic field. We present a detailed study of the ICME in a TGG crystal showing the dependence of the measured effect on the light intensity, the optical polarization, and on the external magnetic field. We derive a relation between the Cotton-Mouton and Inverse CottonMouton effects that is roughly in agreement with existing experimental data. Our results open the way to applications of the ICME in optical devices.The Inverse Cotton-Mouton Effect (ICME) is a magnetization induced in any medium by a non resonant linearly polarized light beam propagating in the presence of a transverse magnetic field. This magnetization is proportional to the value of the magnetic field, and to the intensity of the propagating electromagnetic waves (see ref.[1] and refs. therein). The ICME was predicted for atomic and molecular systems [2] and for the quantum vacuum [3]. As stated in ref.[1], microscopically, the light-induced dc magnetization arises because the optical field shifts the different magnetic states of the ground manifold differently, and mixes into these ground states different amount of excited states.As shown in ref.[3] the ICME is related to the term in the expansion of the electromagnetic energy of the medium U which is quadratic in the electric and in the magnetic field, which can be written as:where ǫ 0 is the vacuum permittivity, µ 0 the vacuum permeability, χ αβγδ is the second order magnetic and electric susceptibility, f α , f β the local electric field factors, E the electric field and B the magnetic field. Einstein summation is assumed and ( α, β, γ, δ) = x, y, z. Assuming Kleinman symmetry [1], the medium magnetization can be finally calculated using the relation M = − ∂U ∂B .