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.
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.
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.
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.
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