© The Royal Society of Chemistry 2018. Large magnetoelectric effects are observed in as-sputtered (nanoparticulate-like) and electrochemically dealloyed (nanoporous) 200 nm thick Fe-Cu films. Application of positive voltages decreases both the saturation magnetization (MS) and coercivity (HC) of the films, while negative voltages cause the reverse effect (increase of MS and HC). The relative variations are as high as 20% for MS and beyond 100% for HC, both for the as-sputtered and dealloyed states. These changes in magnetic properties are caused by controlled and reversible electric-field-driven nanoscale phase transformations between face-centered cubic (fcc) and body-centered cubic (bcc) structures. These phase transitions are in turn due to selective redox reactions induced by the applied voltage, which can be regarded as a "magnetoionic effect." The controlled tuning of HC and MS with the moderate values of applied voltage, together with the sustainable composition of the investigated alloys (not containing noble metals, as opposed to many previous works on magnetoelectric effects in thin films), pave the way towards the implementation of magnetic and spintronic devices with enhanced energy efficiency and functionalities.