The Fe(CoB)/MgO interface is vital to spintronics as it exhibits the tunneling magnetoresistance (TMR) effect and interfacial perpendicular magnetic anisotropy (PMA) simultaneously. To further enhance TMR and PMA for the development of high-density magnetoresistive random access memory, it is essential to clarify the behavior of Fe atoms interfaced with MgO. This study reveals that the spin and orbital magnetic moments of Fe are enhanced at the Fe/MgO interface. The enhancement in the orbital magnetic moment is much more significant than that predicted by the standard density functional theory. Theoretical calculations based on the orbital polarization correction reproduce this enhancement, the origin of which is attributed to the electron-electron correlation resulting from electron localization at the Fe/MgO interface. The present findings highlight the importance of electro--electron correlation at ferromagnet/oxide interfaces, which has often been disregarded in spintronics, and provide a new perspective in materials design.