The large male was filmed striking its flippers together off the coast of the Farne Islands during the breeding season in 2017.
While captive seals can be seen clapping in zoos and aquariums, scientists say this is the first time one of their wild counterparts has been seen on camera performing the action.
While humans clap to applaud, in the case of wild grey seals, this gesture signifies the opposite.
Scientists believe male seals clap to demonstrate strength as part of an attempt to ward off competitors and attract mates.
The action produces a “loud high-frequency noise”, sending out “a clear signal” to other males.
In the video, the seal can be seen swimming close to a female, with other males lurking nearby, before it starts clapping.
Dr Ben Burville, a researcher at the University of Newcastle, who took the footage, said: “The effect of the clap was instant and the rival males rapidly dispersed.
“The clap was incredibly loud and at first I found it hard to believe what I had seen.”
Dr Burville, who had been trying for years to capture clapping seals on camera, added: “I’ve heard the distinctive shotgun-like cracks many times over the years and I felt sure this clapping behaviour was the source, but filming the seals in action has eluded me for 17 years.
“Then one day I had heard a couple of claps in the distance, I just hit the record button and eureka!”
The video is part of an international study published in the journal Marine Mammal Science.
Dr David Hocking, from Monash University in Australia, who led the study, said: “The discovery of ‘clapping seals’ might not seem that surprising, after all, they’re famous for clapping in zoos and aquaria.
“But where zoo animals are often trained to clap for our entertainment these grey seals are doing it in the wild of their own accord.”
The researchers say understanding more about grey seals and other marine life could help protect the species against the harmful effects of pollution.
Dr Hocking added: “Clapping appears to be an important social behaviour for grey seals, so anything that disturbed it could impact breeding success and survival for this species.”