Materials in which magnetic order and electric fields can be coupled are of high fundamental and technological interests. Electrical control of magnetism is not only important for ultralow power consumption applications, but also enables control over intrinsic material properties that may have a major step in new developments in spintronic and magnetoelectric devices. Here we show that the magnetism induced by aryl-radicals covalently functionalized on top of multilayer graphene is sensitive to external electric fields which coupled to the interlayer charge-imbalance yields a strong magnetoelectric coupling. We used first-principles simulations, taking into account van der Waals dispersion forces, to show that this effect is thickness-dependent: it increases dramatically to thicker graphene structures reaching magnetoelectric coefficients comparable to perovskite interfaces. The interplay between electric fields and magnetism also leads functionalized graphene layers to a fully polarized spin state (half-metallicity). Efficiency nearly to 100% spin-polarization is observed at low electric bias, and the selection of the spin-conducting channel is determined by the field polarization.