  Let $m$ be a positive integer and let $\Omega$ be a finite set. The
$m$-closure of $G\leq\operatorname{Sym}(\Omega)$ is the largest permutation
group on $\Omega$ having the same orbits as $G$ in its induced action on the
Cartesian product $\Omega^m$. The $1$-closure and $2$-closure of a solvable
permutation group need not be solvable. We prove that the $m$-closure of a
solvable permutation group is always solvable for $m\geq3$.
