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