The notion of Abelian Kernel of a finite monoid extends the notion of derived subgroup of a finite group. In this line, an extension of the notion of solvable group to idempotent commuting monoids is quite natural: the solvable monoids are the monoids such that the chain of iterated Abelian kernels ends with the set of idempotents. We prove that the finite idempotent commuting monoids satisfying this property are precisely those whose subgroups are solvable.