To address the problems of strong noise contamination and weak feature representation in leakage magnetic field signals for early transformer fault identification, as well as the reliance of variational mode decomposition (VMD) parameters on manual tuning and the tendency of traditional intelligent optimization methods to fall into local optima, an early fault identification approach is proposed by optimizing VMD using chaotic evolution optimization (CEO) and integrating wavelet threshold (WT) denoising with support vector machine (SVM) classification. Taking envelope entropy minimization as the objective function, CEO is employed to adaptively search for the optimal VMD parameters, including the mode number K and penalty factor α, thereby obtaining stable band-limited mode decomposition. On this basis, WT denoising is further applied to suppress residual narrowband periodic interference, enabling robust reconstruction of the leakage magnetic field signal. According to the axial distribution characteristics of the leakage magnetic field, a feature vector is constructed, and an RBF-kernel SVM is used to identify the type and location of six typical incipient faults. Results from ANSYS simulations and dynamic experiments based on fiber-optic magneto-optic measurement demonstrate that the envelope-entropy reduction achieved by the proposed CEO approach outperforms particle swarm optimization (PSO) and the firefly algorithm (FA). Under the same diagnostic framework, the proposed CEO-VMD-WT-SVM method achieves an accuracy exceeding 98% and exhibits superior overall performance compared with manual parameter selection, PSO, and FA, providing an efficient and practical solution for online early transformer fault diagnosis.