Uniquely in Cu2OSeO3, the Skyrmions, which are topologically protected magnetic spin vortexlike objects, display a magnetoelectric coupling and can be manipulated by externally applied electric (E) fields. Here, we explore the E-field coupling to the magnetoelectric Skyrmion lattice phase, and study the response using neutron scattering. Giant E-field induced rotations of the Skyrmion lattice are achieved that span a range of similar to 25 degrees. Supporting calculations show that an E-field-induced Skyrmion distortion lies behind the lattice rotation. Overall, we present a new approach to Skyrmion control that makes no use of spin-transfer torques due to currents of either electrons or magnons.