  We introduce the class of split regular Hom-Leibniz algebras as the natural
generalization of split Leibniz algebras and split regular Hom-Lie algebras. By
developing techniques of connections of roots for this kind of algebras, we
show that such a split regular Hom-Leibniz algebra $L$ is of the form $L = U +
\sum\limits_{[j] \in \Lambda/\sim}I_{[j]}$ with $U$ a subspace of the abelian
subalgebra $H$ and any $I_{[j]}$, a well described ideal of $L$, satisfying
$[I_{[j]}, I_{[k]}] = 0$ if $[j]\neq [k]$. Under certain conditions, in the
case of $L$ being of maximal length, the simplicity of the algebra is
characterized.
