The Faraday effect (FE) of the rare-earth (RE) paramagnetic garnet crystals associated with magnetic-dipole (MD) transitions has been investigated theoretically over a wide temperature range 80 to 300 K. Over this temperature range, the “gyromagnetic” Verdet V gm (m) of the Eu3Ga5O12 (EuGG) is not a linear function of the magnetic susceptibility χ measured along the [111] axis. We find that the nontrivial character of the temperature dependence of the MD Verdet constant V gm (m) is associated with the presence of a contribution to the Faraday rotation of the Van Vleck “mixing” by an external magnetic field of the Eu3+ electronic states. The optical absorption and magnetic circular dichroism (MCD) of Eu3+ ion in EuGG at 85 K for the MD transition 7 F 0 → 5 D 1 were measured along the [111] axis. We show that the appearance of the MCD feature observed for the absorption line near 526.6 nm for the 7 F 0 → 5 D 1 MD absorption band may be well-explained by the contribution of Van Vleck “mixing” between the Stark singlet states from the 7 F 0 and 7 F 1 multiplet manifolds mixed by the external magnetic field H.