Our ab initio studies show clear evidence that magnetic anisotropy (MA) and the direction of magnetization in metallic magnetic multilayers can be tailored at once by surface charging. By taking Fe-Pt multilayers as a representative example, we demonstrate that surface charging has a deep effect on the magnitude of the MA, which is composition dependent, achieving remarkably large values for systems featuring a single Fe layer capped with Pt. More intriguing is the behavior of the multilayers capped with iron bilayers, for which surface charging not only affects the value of the anisotropy but an easy-axis switching is also revealed. By analyzing the electronic structure of the magnetic layers and relating the MA to the orbital moment anisotropy, some insights about the origin of the MA from a local perspective can be inferred.