It's true by definition, there's really nothing more to it than that.
Angular velocity does not have to be represented by a vector, though it can be in 3 dimensions. We choose to represent it by the vector
$\vec{w} = \vec{r} \times \vec{v}$
And therefore following the cyclic properties of any cross product, it must be true that
$\vec{v} = \vec{w} \times \vec{r}$