Coast Guard and Customs Service divers located the remains near the central part of the ship, where survivors had said the two were last seen.
Specialized police divers were going into the sea to remove the remains, which will be examined by forensic experts on the mainland in Tuscany. DNA testing could take a few days, authorities said.
The side of the ship where the remains were found is badly smashed in after lying submerged since it capsized on Jan. 13, 2012.
Experts plan to go inside the ship, retrieve some of the Concordia's computers, and try to determine why backup generators and some other equipment failed to work immediately after the collision.
The Concordia's captain, Francesco Schettino, is on trial for alleged manslaughter, causing the shipwreck and abandoning ship during a confused and delayed evacuation. Prosecutors contend he deliberately went off the route, bringing the ship too close to Giglio's rocky coastline at night. The captain, who risks 20 years in prison, contends that the reef wasn't on the ship's nautical charts.
In separate proceedings, five other employees of the Italian cruise company, Costa Concordia SpA, were allowed to make plea bargains in exchange for lenient sentences. But a Florence prosecutor this week challenged those sentences, and Italy's highest criminal court will eventually rule on that.