Context. The amount of adaptive optics (AO) telemetry generated by visible/near-infrared ground-based observatories is ever greater, leading to a growing need for a standardised data exchange format to support performance analysis, AO research, and development activities that involve large-scale telemetry mining, processing, and curation. Aims. This paper introduces the Adaptive Optics Telemetry (AOT) data exchange format as a standard for sharing AO telemetry from visible/infrared ground-based observatories. AOT is based on the flexible image transport system (FITS) and aims to provide unambiguous and consistent data access across various systems and configurations, including natural and single- or multiple-laser guide-star AO systems. Methods. We designed AOT with a focus on two key use cases: atmospheric turbulence parameter estimation and point-spread function reconstruction. We prototyped and tested the design using existing AO telemetry datasets from multiple systems: single conjugate with natural and laser guide stars, tomographic systems with multi-channel wavefront sensors, and single- and multi-wavefront correctors in systems featuring either a Shack-Hartmann or Pyramid as the main wavefront sensor. Results. The AOT file structure has been thoroughly defined, with specified data fields, descriptions, data types, units, and expected dimensions. To support this format, we have developed a Python package that enables the data conversion, reading, writing, and exploration of AOT files; it has been made publicly available and is compatible with a general-purpose Python package manager. We have demonstrated the flexibility of the AOT format by packaging data from five different instruments, installed on different telescopes.