The translation of brain dynamics into natural language is pivotal for brain-computer interfaces (BCIs), a field that has seen substantial growth in recent years. With the swift advancement of large language models, such as ChatGPT, the need to bridge the gap between the brain and languages becomes increasingly pressing. Current methods, however, require eye-tracking fixations or event markers to segment brain dynamics into word-level features, which can restrict the practical application of these systems. These event markers may not be readily available or could be challenging to acquire during real-time inference, and the sequence of eye fixations may not align with the order of spoken words. To tackle these issues, we introduce a novel framework, DeWave, that integrates discrete encoding sequences into open-vocabulary EEG-to-text translation tasks. DeWave uses a quantized variational encoder to derive discrete codex encoding and align it with pre-trained language models. This discrete codex representation brings forth two advantages: 1) it alleviates the order mismatch between eye fixations and spoken words by introducing text-EEG contrastive alignment training, and 2) it minimizes the interference caused by individual differences in EEG waves through an invariant discrete codex. Our model surpasses the previous baseline (40.1 and 31.7) by 3.06% and 6.34\%, respectively, achieving 41.35 BLEU-1 and 33.71 Rouge-F on the ZuCo Dataset. Furthermore, this work is the first to facilitate the translation of entire EEG signal periods without the need for word-level order markers (e.g., eye fixations), scoring 20.5 BLEU-1 and 29.5 Rouge-1 on the ZuCo Dataset, respectively.