In the sense of eigenstructure (eigenvalues/eignenvectors) assignment, the effectiveness and disturbance suppressibility of a controller depend mainly on the left eigenstructure (eignevalues/left eigenvectors) of a system. On the other hand, the disturbance decouplability is governed by the right eigenstructure (eignevalues/right eigenvectors) of the system. In this paper, in order to obtain a disturbance decouplable as well as effetive and disturbance suppressible controller, a concurrent assignment methodology of the left and right eigenstructure is proposed. The biorthogonality condition between the left and right modal matrix and state selection matrices are used to develop the methodology. The proposed concurrent eigenstructure assignment methodology guarantees that the desired eigenvalues are achieved exactly and the desired left and right eigenvectors are assigned to the best possible (achievable) sets of eigenvectors in the least square sense, respectively. A numerical example is presented to illustrate the validity and usefulness of the proposed methodology.