  In this paper we show that the method for describing solvable Lie algebras
with given nilradical by means of non-nilpotent outer derivations of the
nilradical is also applicable to the case of Leibniz algebras. Using this
method we extend the classification of solvable Lie algebras with naturally
graded filiform Lie algebra to the case of Leibniz algebras. Namely, the
classification of solvable Leibniz algebras whose nilradical is a naturally
graded filiform Leibniz algebra is obtained.
