Voltage control of magnetoresistance (MR) in nanoscale three-dimensional (3D) geometries is interesting from a fundamental point of view and a promising route toward novel sensors and energy-efficient computing schemes. Magneto-ionic mechanisms are favorable for low-voltage control of magnetism and room-temperature operation, but magneto-ionic control of MR has been studied only for planar geometries so far. We synthesize a 3D nanomaterial with magneto-ionic functionality by electrodepositing an iron hydroxide/iron coating on a porous nanoscale gold network (aerogel). To enable maximum magneto-ionic ON-OFF-switching, the thickness of the coating is adjusted to a few nanometers by a self-terminating electrodeposition process. In situ magnetotransport measurements during electrolytic gating of these nanostructures reveal large reversible changes in MR, including ON-OFF-switching of MR, with a small applied voltage difference (1.72 V). This effect is related to the electrochemical switching between a ferromagnetic iron shell/gold core nanostructure (negative MR at the reduction voltage) and an iron oxide shell/gold core nanostructure (negligible MR at the oxidation voltage).