Electrical control of magnetism is a long-standing goal in science and technology, with the potential to enable a next generation of low-power memory and logic devices. Recently developed electrolyte gating techniques provide a promising route to realization, although the ultimate limits on modulation of magnetic properties remain unknown. Here, guided by a recent theoretical prediction, we demonstrate large enhancement of electrostatic modulation of ferromagnetic order in ion-gel-gated ultrathin films of the perovskite La0.5Sr0.5CoO3−δ by thickness tuning to the brink of percolation. Application of only 3–4 V is then shown capable of inducing a clear percolation transition from a short-range magnetically ordered insulator to a robust long-range ferromagnetic metal with perpendicular magnetic anisotropy. This realizes giant electrostatic Curie temperature modulation over a 150 K window, outstanding values for both complex oxides and electrolyte gating. In operando polarized neutron reflectometry confirms gate-controlled ferromagnetism, additionally demonstrating, surprisingly, that electrostatically induced magnetic order can penetrate substantially deeper than the Thomas-Fermi screening length.