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A submanifold in a real space form attaining equality in the DDVV inequalityat every point is called a Wintgen ideal submanifold. They are invariantobjects under the Moebius transformations. In this paper, we classify thoseWintgen ideal submanifolds of dimension m>3 which are Moebius homogeneous.There are three classes of non-trivial examples, each related with a famousclass of homogeneous minimal surfaces in $S^n$ or $CP^n$: the cones over theVeronese surfaces $S^2$ in $S^n$, the cones over homogeneous flat minimalsurfaces in $S^n$, and the Hopf bundle over the Veronese embeddings of $CP^1$in $CP^n$.

Classification of Moebius homogeneous Wintgen ideal submanifolds