Biological signals, such as electroencephalograms (EEG), play a crucial role in numerous clinical applications, exhibiting diverse data formats and quality profiles. Current deep learning models for biosignals (based on CNN, RNN, and Transformers) are typically specialized for specific datasets and clinical settings, limiting their broader applicability. This paper explores the development of a flexible biosignal encoder architecture that can enable pre-training on multiple datasets and fine-tuned on downstream biosignal tasks with different formats.To overcome the unique challenges associated with biosignals of various formats, such as mismatched channels, variable sample lengths, and prevalent missing val- ues, we propose Biosignal Transformer (BIOT). The proposed BIOT model can enable cross-data learning with mismatched channels, variable lengths, and missing values by tokenizing different biosignals into unified "sentences" structure. Specifically, we tokenize each channel separately into fixed-length segments containing local signal features and then rearrange the segments to form a long "sentence". Channel embeddings and relative position embeddings are added to each segment (viewed as "token") to preserve spatio-temporal features.The BIOT model is versatile and applicable to various biosignal learning settings across different datasets, including joint pre-training for larger models. Comprehensive evaluations on EEG, electrocardiogram (ECG), and human activity sensory signals demonstrate that BIOT outperforms robust baselines in common settings and facilitates learning across multiple datasets with different formats. Using CHB-MIT seizure detection task as an example, our vanilla BIOT model shows 3% improvement over baselines in balanced accuracy, and the pre-trained BIOT models (optimized from other data sources) can further bring up to 4% improvements. Our repository is public at https://github.com/ycq091044/BIOT.