In bistable vision, subjective perception wavers between two interpretations of a constant ambiguous stimulus. This dissociation between conscious perception and sensory stimulation has motivated various empirical studies on the neural correlates of bistable perception, but the neurocomputational mechanism behind endogenous perceptual transitions has remained elusive. Here, we recurred to a generic Bayesian framework of predictive coding and devised a model that casts endogenous perceptual transitions as a consequence of prediction errors emerging from residual evidence for the suppressed percept. Data simulations revealed close similarities between the model's predictions and key temporal characteristics of perceptual bistability, indicating that the model was able to reproduce bistable perception. Fitting the predictive coding model to behavioural data from an fMRI-experiment on bistable perception, we found a correlation across participants between the model parameter encoding perceptual stabilization and the behaviourally measured frequency of perceptual transitions, corroborating that the model successfully accounted for participants' perception. Formal model comparison with established models of bistable perception based on mutual inhibition and adaptation, noise or a combination of adaptation and noise was used for the validation of the predictive coding model against the established models. Most importantly, model-based analyses of the fMRI data revealed that prediction error time-courses derived from the predictive coding model correlated with neural signal time-courses in bilateral inferior frontal gyri and anterior insulae. Voxel-wise model selection indicated a superiority of the predictive coding model over conventional analysis approaches in explaining neural activity in these frontal areas, suggesting that frontal cortex encodes prediction errors that mediate endogenous perceptual transitions in bistable perception. Taken together, our current work provides a theoretical framework that allows for the analysis of behavioural and neural data using a predictive coding perspective on bistable perception. In this, our approach posits a crucial role of prediction error signalling for the resolution of perceptual ambiguities.