Matthew Myburgh, 16, and Charlie Morrell, 15, were standing on a ledge jutting into the sea at Lulworth Cove, Dorset, either fishing or watching the stormy seas when a wave swept them away.
Their friend Richard Lawrence, 15, who was standing on a ledge higher up on the western tip of the cove, jumped into the sea to try to save them.
He clung to a buoy before swimming back to the shore and raising the alarm at 7.20pm on November 3.
Assistant Chief Constable Adrian Whiting, of Dorset Police, said: "Sadly, a body believed to be one of the two missing boys has been found in shingle in Lulworth Cove.
"A local man made the discovery and called the police at 7.41am this morning."
The families of the two boys were being kept up to date with developments and the identity of the body has yet to be confirmed.
More than 100 people, including coastguard rescue teams, Dorset Police, divers from Avon and Somerset Police, and friends of the boys, have been searching for them since they were swept away six days ago.
Experts estimated the boys, both from West Lulworth, could only have survived for three hours in the water.
Dorset Police have said that Richard, who suffered a hand injury, was highly traumatised" by the tragedy.
Locals in the community of about 800 people have said the storm that night was one of the worst in living memory.
Heavy rain and gusts of nearly 70mph battered the south coast of England on November 3, with reports of 9ft waves and a force nine gale in picturesque Lulworth Cove, a Unesco-designated World Heritage Site.
The two boys attended The Purbeck School, in Wareham, Dorset.Reuse content