The automatic deformation of the computational mesh along with the deformed geometry in design optimization cycles is a valuable procedure, as it reduces the required time for the construction of new meshes. The introduction of harmonic coordinates for the deformation of objects included within a closed mesh (cage) has been introduced in computer graphics. Harmonic coordinates result from solutions to the Laplace’s equation (harmonic functions) using a numerical solver. In this work, a modification to the classical harmonic coordinates’ concept is introduced for the deformation of 2D geometries (and the corresponding computational mesh) which are defined as B-spline curves. The B-spline basis functions are used as harmonic functions along the mesh boundary, being also the geometry to be deformed. Thus, any deformation of the B-spline boundary, through the movement of the curve’s control points, can be successfully propagated to the interior of the computational domain, resulting in the concurrent and conformable modification of the B-spline boundary and the entire computational mesh. For the computation of harmonic coordinates a node-centered Finite-Volume based Laplace solver for unstructured meshes is used, enhanced with an agglomeration multigrid scheme. The proposed method is applied and assessed for the shape and mesh morphing of airfoils.