Video from the imperial eagle, Darshan, was live-streamed as it swooped 829.8 metres to its trainer on the ground.
The organisers, Freedom Conservation, claim it is the highest-ever recorded bird flight from a man-made structure.
The event was staged to highlight the plight of the endangered bird of prey.
Although the camera weighed only 300g, that still equates to 10% of the bird's weight.
Darshan has been trained by falconer Jacques-Olivier Travers from a breeding facility in Thonon, France.
After guiding the bird down he described the flight "as perfect."
Freedom Conservation hope that the flight will be a symbol that humans and nature can live together.
"This eagle is a signal that things can change. It was once endangered, but after conservation programmes it is not so endangered," the Director of Freedom Conservation Ronald Menzel told the BBC, which was given exclusive access to the live video stream.
An eagle with a small camera on its back has flown from the top of the world's tallest building, the Burj Khalifa skyscraper in Dubai.