Departing from traditional linguistic models, advances in deep learning have resulted in a new type of predictive (autoregressive) deep language models (DLMs). Using a self-supervised next-word prediction task, these models generate appropriate linguistic responses in a given context. In the current study, nine participants listened to a 30-min podcast while their brain responses were recorded using electrocorticography (ECoG). We provide empirical evidence that the human brain and autoregressive DLMs share three fundamental computational principles as they process the same natural narrative: (1) both are engaged in continuous next-word prediction before word onset; (2) both match their pre-onset predictions to the incoming word to calculate post-onset surprise; (3) both rely on contextual embeddings to represent words in natural contexts. Together, our findings suggest that autoregressive DLMs provide a new and biologically feasible computational framework for studying the neural basis of language.