The species, belonging to a group more commonly known as shadowdamsels, has been named Mesosticta davidattenboroughi.
Researchers decided to name the new species after David Attenborough because of his long-standing appreciation of dragonflies, and to celebrate his 90th birthday.
Mesosticta davidattenboroughi joins a long list of animals which have been named after Sir David Attenborough, including a weevil and fossil species of a plesiosaur and a fish.
The finding, described in the Journal of Systematic Palaeontology, was made in the Hukawng Valley of Kachin Province in Myanmar. The fossil was found in a piece of mid- Cretaceous Burmese amber.
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"Sir David was delighted because he is not only interested in the story of amber, but also a president of the British Dragonfly Society," he added.
The fossil itself is extremely well preserved as it is encased in yellow transparent amber and includes a complete set of wings, researchers said.
"Mesosticta davidattenboroughi is quite unique because we have uncovered a new species and it confirms the previous attribution of Mesosticta to the Platystictidae," said Daran Zheng from Nanjing Institute of Geology and Palaeontology.
"It is the first fossil group of modern platystictid damselflies and documents the appearance of Platystictidae as early as mid-Cretaceous," said Zheng.