Mg-codoped Lu3Al5O12:Ce single crystal scintillators were prepared by a micropulling down method in a wide concentration range from 0 to 3000 ppm of Mg codopant. Their structure and chemical composition were checked by X-ray diffraction and electron probe microanalysis techniques. Absorption and luminescence spectra, photoluminescence decays, and thermoluminescence glow curves were measured together with several other scintillation characteristics, namely, the scintillation decay, light yield, afterglow, and radiation damage to reveal the effect of Mg codoping. Several material characteristics manifest a beneficial effect of Mg codopant. We propose a model explaining the mechanism of material improvement which is based on the stabilization of a part of the cerium dopant in the tetravalent charge state. The stable Ce4+ center provides an additional fast radiative recombination pathway in the scintillation mechanism and efficiently competes with electron traps in garnet scintillators.