Interfacial magnetoelectric coupling is a viable path to achieve electrical writing of magnetic information in spintronic devices. For the prototypical Fe/BaTiO3 system, only tiny changes of the interfacial Fe magnetic moment upon reversal of the BaTiO3 dielectric polarization have been predicted so far. Here, by using X-ray magnetic circular dichroism in combination with high-resolution electron microscopy and first principles calculations, we report on an undisclosed physical mechanism for interfacial magnetoelectric coupling in the Fe/BaTiO3 system. At this interface, an ultrathin oxidized iron layer exists, whose magnetization can be electrically and reversibly switched on and off at room temperature by reversing the BaTiO3 polarization. The suppression/recovery of interfacial ferromagnetism results from the asymmetric effect that ionic displacements in BaTiO3 produces on the exchange coupling constants in the interfacial-oxidized Fe layer. The observed giant magnetoelectric response holds potential for optimizing interfacial magnetoelectric coupling in view of efficient, low-power spintronic devices.