Discovering fundamentally new ways to manipulate magnetic spins is crucial for research into advanced technologies. Magnetic Skyrmions, which are topologically stable whirls of magnetic spins, are promising candidates for new device components since those found in metallic host materials can be manipulated using electric currents. In this paper, we demonstrate that in the insulating material Cu2OSeO3, the inherent magnetoelectric coupling allows the Skyrmions to be controlled using electric fields. This coupling is immediately attractive for applications, since the control of Skyrmions by electric fields is in principle more efficient than by using electric currents. Using small-angle neutron scattering, we report the observation of giant electric field-induced Skyrmion lattice rotations, and explain our observations with supporting theory. The new physics revealed from our work is that the Skyrmion lattice rotations are caused by an electric field-induced distortion of the Skyrmion shape. This corresponds to an entirely new approach for controlling Skyrmions in general; in all other experimental work until now Skyrmion motion could only be initiated by harnessing the forces provided by dissipative flows of either conduction electrons or magnons. Therefore our study establishes the principles behind a new Skyrmion control paradigm that can be exploited for the development of energy efficient Skyrmion-based applications.