Large synchronous generators are the heart of the modern world, while producing the vast majority of the electric power consumed globally. Although they are robust devices, they are prone to degradation and failure. If such failures are not detected at an early stage, then the negative impact may be catastrophic in terms of financial costs, repair times, human lives and quality of life. This is the reason for continuous research in the field of condition monitoring aiming towards the reliable operation of synchronous generators. This paper proposes a novel technique for the diagnosis of the static eccentricity in synchronous generators. The proposed approach is off-line and non-intrusive, allowing the estimation of the fault severity with stator current measurements only. The performed work has been carried out with Finite Element Simulations and extensive experimental testing.