In this article, an online unified solution based on stochastic configuration network (SCN) and Levenberg- Marquardt (LM) algorithm is proposed to generate optimal switching angles for selective harmonic elimination (SHE) in both the symmetric and asymmetric cascaded H-bridge (CHB) multilevel inverters (MLIs). Different from the traditional neural network framework for SHE, this unified solution uses SCN to only generate initial values of the switching angles online, which significantly reduce the precision demand on training SCN and avoids the local optima problem of gradient descent algorithm. After obtaining the initial values from SCN online, the LM algorithm can be used to rapidly solve the exact switching angles for SHE, which guarantees the solving efficiency and precision of the final solutions. Moreover, the stability of the proposed method is proved via Newton-like convergence theory. Compared with intelligent search algorithms and look-up table method, the proposed solution can not only online generate optimal theoretical switching angles but with much fewer data storage space. Experimental results of both symmetric and asymmetric MLI cases are presented to validate the correctness and online applicability of the proposed solution.