The 28-year-old father of a three-year-old girl was recovered off Aughris Head, known locally as Roguey Point, in Bundoran.
Some 120 soldiers, as well as a Navy diving unit and divers from Donegal, Sligo, and Enniskillen, searched for Mr Carey, known as Care Bear, who was swept away by a rip-tide in five-metre waves last Tuesday evening.
He was on a swimming break from nearby Finner military camp, with four other soldiers.
Mr Carey and another man got into difficulty swimming off a corner of Tullan Strand, beneath beneath Roguey cliff, a favourite walking spot. Eye-witness, Mel Fallon, from Bundoran, said Mr Carey was swept out to sea, and the other man survived with an injured leg because he was swept onto the cliff-bottom rocks.
A Sligo-based Coastguard helicopter and an Air Corps AW139 helicopter participated in the six-day search.
So did the Bundoran life-boat and the Killybegs life boat. Mr Carey, attached to Custume barracks, in Athlone, but from the Mullingar area, was on a training course at Finner camp. Dara O’Malley Daly, station manager at Malin Head Coast Guard, said: “We would like to offer our condolences to the man’s family.”