Shane Davies, 33, went missing at about 3.30pm on Saturday (12 June) after becoming separated from his friend as they swam to shore, police said.
Coastguard and police conducted extensive searches of the area.
Sadly, on Sunday morning (13 June) a body was found in the water which is believed to be Shane, said police.
Next of kin have been informed and the matter has been passed to the Coroner's Office.
Inspector Oliver Pullen said: "Our thoughts are with Shane's family at this incredibly difficult time.
"I'd like to thank Coastguard and other colleagues for their work to help find Shane."