In the present study a digital twin-based methodology for Structural Health Monitoring (SHM) of composite stiffened panels is developed. More specifically, beyond damage detection and localization, the quantification of damage is determined based on relevant damaged training data provided by a numerical campaign. Parametric finite element models with distinct damage morphologies, i.e. skin-to-stringer delaminations, are generated based on a Latin hypercube sampling plan. The above sampling plan generates an adequate amount of simulated strain data capable of establishing a relation among the damage characteristics, i.e. damage size and location, and the longitudinal strain at specific sensing locations. Hence, Gaussian process (GP) surrogate models are trained with the numerically generated data and their hyperparameters are determined via Bayesian optimization. The damage quantification is treated as a minimization problem, the solution of which is obtained via a global optimization iterative procedure. The methodology is assessed utilizing a single-stringer composite panel with a rectangle skin/stringer artificial delamination. Compressive loads are applied on the panel and longitudinal static strains are received by permanently fiber Bragg grating sensors affixed onto the stringer feet. The pre-trained GP models are fed with experimental strains during testing and in turn yield the damage characteristics of the delamination. The methodology is also applicable to unknown load conditions as it predicts the load acting on the panel on the first SHM levels. Promising results are obtained, empowering the viewpoint of the proposed methodology which aims to harness the contemporary capabilities of numerical models toward real-time damage diagnosis on complicated structures.