We study the problem of integrating cognitive language processing signals (e.g., eye-tracking or EEG data) into pre-trained language models like BERT. Existing methods typically fine-tune pre-trained models on cognitive data, ignoring the semantic gap between the texts and cognitive signals. To fill the gap, we propose CogBERT, a framework that can induce fine-grained cognitive features from cognitive data and incorporate cognitive features into BERT by adaptively adjusting the weight of cognitive features for different NLP tasks. Extensive experiments show that: (1) Cognition-guided pre-trained models can consistently perform better than basic pre-trained models on ten NLP tasks. (2) Different cognitive features contribute differently to different NLP tasks. Based on this observation, we give a fine-grained explanation of why cognitive data is helpful for NLP. (3) Different transformer layers of pre-trained models should encode different cognitive features, with word-level cognitive features at the bottom and semantic-level cognitive features at the top. (4) Attention visualization demonstrates that CogBERT aligns with human gaze patterns and improves its natural language comprehension ability.