Operating large-scale scientific facilities often requires fast tuning and robust control in a high dimensional space. In this paper we introduce a new physics-informed optimization algorithm based on Gaussian process regression. Our method takes advantage of the existing domain knowledge in the form of realizations of a physics model of the observed system. We have applied a physics-informed Gaussian Process method experimentally at the SPEAR3 storage ring to demonstrate online accelerator optimization. This method outperforms Gaussian Process trained on data as well as the standard approach routinely used for operation, in terms of convergence speed and optimal point. The proposed method could be applicable to automatic tuning and control of other complex systems, without a prerequisite for any observed data.