In this letter a new Lagrangian variational principle is proved to hold for the Einstein field equations, in which the independent variational tensor field is identified with the Ricci curvature tensor R mu. rather than the metric tensor g mu.. The corresponding Lagrangian function, denoted as L R, is realized by a polynomial expression of the Ricci 4-scalar R = g mu. R mu. and of the quadratic curvature 4scalar. = R mu. R mu.. The Lagrangian variational principle applies both to vacuum and non-vacuum cases and for its validity it demands a non-vanishing, and actually also positive, cosmological constant similar to > 0. Then, by implementing the deDonder-Weyl formalism, the physical conditions for the existence of amanifestly-covariant Hamiltonian structure associated with such a Lagrangian formulation are investigated. As a consequence, it is proved that the Ricci tensor can obey a Hamiltonian dynamics which is consistent with the solutions predicted by the Einstein field equations.