We discuss an interplay between T-duality and integrability for certain classical non-linear sigma models. In particular, we consider strings on the AdS₅ × S⁵ background and perform T-duality along the four isometry directions of AdS₅ in the Poincaré patch. The T-dual of the AdS₅ sigma model is again a sigma model on an AdS₅ space. This classical T-duality relation was used in the recently uncovered connection between light-like Wilson loops and MHV gluon scattering amplitudes in the strong coupling limit of the AdS/CFT duality. We show that the explicit coordinate dependence along the T-duality directions of the associated Lax connection (flat current) can be eliminated by means of a field dependent gauge transformation. As a result, the gauge equivalent Lax connection can easily be T-dualized, i.e. written in terms of the dual set of isometric coordinates. The T-dual Lax connection can be used for the derivation of infinitely many conserved charges in the T-dual model. Our construction implies that local (Noether) charges of the original model are mapped to non-local charges of the T-dual model and vice versa.