In spintronics, ordered magnetic domains are important for magnetic microdevices and controlling the orientation of ordered magnetic domains is important for applications such as domain wall resistance and spin wave propagation. Although a magnetic field or a current can reorient ordered magnetic domains, an energy-efficient electric-field-driven rotation of the ordered magnetic domains remains elusive. Here, using a nanotrenched polymeric layer, we obtain ordered magnetic strip domains in Ni films on a ferroelectric substrate. By applying electric fields to the ferroelectric substrate, we demonstrate that the ordered magnetic strip domains in Ni films are switched between the y- and x-axes driven by electric-fields. This switching of magnetic strip orientation is attributed to the electric-field-modulated in-plane magnetic anisotropies along the x- and y-axes of the Ni films, which are caused by the anisotropic biaxial strain of the ferroelectric substrate via strain-mediated magnetoelectric coupling. These results provide an energy-efficient approach for manipulating the ordered magnetic domains using electric fields.