In the initial stages of wave energy converter development, a wide range of design parameters should be tested and analyzed across all operational sea states. As a result, it is required to conduct a large number of time domain simulations that are computationally expensive. The following study presents the application of a fast and high-fidelity alternative technique, named statistical linearization (SL), that can be used for the stochastic analysis of nonlinear wave energy converters. The method consists of an approximate solution that allows one to quickly estimate the contribution of nonlinear terms using a probabilistic model. The application of the statistical linearization is demonstrated using three conceptually different wave energy converters, a point absorber, an oscillating wave surge converter, and an oscillating water column, with distinct nonlinear dynamics. The performance of SL is assessed against nonlinear time-domain simulations in terms of spatial response distributions and power spectral densities of responses and excitation loads, mean offsets, mean absorbed power and equivalent linear terms. The results show a good agreement between the two types of models for all wave energy converters considered, while showing that SL is approximately 3 to 4 orders of magnitude faster than the time domain model.