This paper considers eigenstructure assignment (ESA) in high-order descriptor linear systems via output feedback. Parametric expressions for the left and right closed-loop eigenvectors associated with the finite closed-loop eigenvalues and two simple and complete parametric solutions to the feedback gain matrix are obtained on the basis of the parametric solution to the generalized high-order Sylvester matrix equation. This approach does not impose any restriction on the closed-loop eigenvalues. The numerical example illustrates the effectiveness of the proposed approach.