Over the last few decades, acoustic fish telemetry has developed into a viable approach for remote monitoring of fish behaviour in the marine environment. Simultaneously, unmanned surface and underwater vehicles have found extensive use as scalable, persistent and cost-effective platforms for ocean observation. Equipping such robotic vehicles with fish telemetry receivers constitutes an emerging approach with the potential to significantly push the current operational limits of fish movement studies at sea. Here, we present an energy-autonomous robotic fish telemetry platform realised through the integration of a real-time acoustic receiver into an ocean-going wave- and solar-powered unmanned surface vehicle. The vehicle frame and energy harvesting solutions are based on the commercially available AutoNaut USV, while the vehicle’s control and communication systems were developed using open-source software and standard hardware components. The open architecture permitted deep integration of the acoustic receiver as a system-level payload making fish detections and other sensor data available in real-time to the vehicle’s onboard control system. The vehicle is thus prepared with local situational awareness to support autonomous control during vehicle-fish encounters, as well as conventional interfaces for remote piloting and data management through long-range wireless communication links and the Internet. The vehicle concept was investigated theoretically and experimentally in an acoustic range test and a full-scale sea trial. When driven passively by waves, tag detection performance was comparable to that of traditional moored receivers, while activation of the auxiliary electric thruster caused a reduction in detection radius of more than 50%, confirming wave-power as the ideal mode of propulsion. Finally, by deploying the AutoNaut over a period of several days at the outskirts of a Norwegian fjord during the seaward migration of Atlantic salmon post-smolts, we demonstrated that the vehicle was able to detect an acoustically tagged post-smolt into the open ocean beyond the reach of the fjord’s stationary receiver grid, while using only wave- and solar energy harvesting to power its operation. The ability to observe small individual fish in the ocean environment using an energy-autonomous robotic vehicle creates novel and unprecedented opportunities for scientific inquiry in fish behaviour and movement ecology studies at sea.