We study the structure of Noetherian Witt rings which are also Gorenstein rings (i.e., have a finite injective resolution). For 1-dimensional Witt rings R, R is Gorenstein iff R is a group ring over \({\mathbb{Z}}\). A number of striking properties are shown to hold for 0-dimensional Gorenstein Witt rings, such as \(ann(ann(I))=I\) for any ideal I. Under an additional assumption on annihilators we show that Gorenstein Witt rings are group ring extensions of Witt rings of local type.