The body was believed to be that of Russel Rebello, an Indian who worked as a waiter on the liner that capsized after it hit rocks off the Italian island of Giglio in January 2012, killing 32 people.
The only other person still missing is Italian passenger Maria Grazia Trecarichi.
The ship was hauled upright last month, giving divers access to parts that had been submerged.
SALVAGE UPDATE: Crews Commence “Winterization” of Costa Concordia Shipwreck
Rebello’s family have told of how the 33-year-old Mumbai native stayed on the ship to help evacuate others.
“I have been waiting for this news for 21 months… We hope that the other lady will immediately be found,” said Rebello’s brother Kevin.
The ship’s captain, Francesco Schettino, is on trial for his role in the disaster and is accused of manslaughter, causing a shipwreck and abandoning ship. His lawyers argue he was not the only person to blame for the accident.
The ship is due to be towed away from the Mediterranean holiday island next spring and broken up into scrap. (Reporting by Naomi O’Leary, editing by Gareth Jones)
© 2013 Thomson Reuters. All rights reserved.