In structural design and structural health monitoring (SHM), the identification of the visco-elastic stiffness tensor of composite materials is considered fundamental, however, the reconstruction of the stiffness coefficients is not straightforward due to the inherent presence of anisotropy and heterogeneity. In the current study, an inverse procedure is proposed based on full field wave dispersion curves to characterize the (18) visco-elastic stiffness parameters of an orthotropic composite plate. The procedure is illustrated by means of finite element method simulations conducted with broadband signals. First, the FEM simulation data, consisting of the in-plane and out-of-plane velocities on the 2D top surface of a composite plate, were converted into the frequency-complex wavenumber domain, including information on elasticity and viscosity, by using the matrix pencil method. The converted data set was then considered as input to a surrogate optimization inversion algorithm, using the semi analytical finite element method (SAFE) as the forward model owing to its accuracy, efficiency and robustness. The full tensorial visco-elastic stiffness parameters were calculated and updated by minimizing the error between the simulated and the calculated complex wavenumbers. The final reconstructed stiffness properties in case of an aluminum plate and of a unidirectional composite laminate show good agreement with the exact input stiffness values, with average errors below 5% for all 18 visco-elastic stiffness parameters.