Inspired by Baxter's perimeter Bethe ansatz I present a method to construct Yangian invariants. The condition for Yangian invariance is formulated as an eigenvalue problem that can be solved using Bethe ansatz techniques. The rather general principle is being worked out for rational inhomogeneous spin-chains with finite-dimensional representations of gl(n) in the quantum space. Using the algebraic Bethe ansatz I derive Bethe ansatz equations for Yangian invariants and study the corresponding on-shell Bethe vectors. They can be interpreted as partition functions of certain vertex models.