In metal/oxide heterostructures, rich chemical, electronic, magnetic and mechanical properties can emerge from interfacial chemistry and structure. The possibility to dynamically control interface characteristics with an electric field paves the way towards voltage control of these properties in solid-state devices. Here, we show that electrical switching of the interfacial oxidation state allows for voltage control of magnetic properties to an extent never before achieved through conventional magneto-electric coupling mechanisms. We directly observe in situ voltage-driven O(2-) migration in a Co/metal-oxide bilayer, which we use to toggle the interfacial magnetic anisotropy energy by >0.75 erg cm(-2) at just 2 V. We exploit the thermally activated nature of ion migration to markedly increase the switching efficiency and to demonstrate reversible patterning of magnetic properties through local activation of ionic migration. These results suggest a path towards voltage-programmable materials based on solid-state switching of interface oxygen chemistry.