Sergio Girotto, a project manager with Italian engineering company Micoperi, which, along with the U.S.-based Titan Salvage, is in charge of the salvage operation, said moving the ship off the rocks was the most delicate phase of the operation, Italy's ANSA news agency reported.
"The first two hours [of the operation] were the most uncertain, because we didn't know precisely how much of the ship was stuck," Girotto said.
The wreckage was moved from the rock reef to a level piece of seabed, Girotto said.
The luxury liner has been on a rock shelf since a 2012 disaster that claimed 32 lives.
Civil Protection Department Chief Franco Gabrielli said cameras and other instruments detected a "major deformation" on the submerged side of the cruise ship during efforts to lift it upright, ANSA reported.
Gabrielli said an assessment on the extent of the damage would be done now that the ship is off the rock shelf.
The first phase of the operation, which was to take about 12 hours, was delayed about 3 hours because of storms, ANSA reported.
Once stabilized upright, the Costa Concordia will be towed and sold for scrap sometime early next year, the report said.
Costa Cruises, which owns the Costa Concordia, said last week the salvage operation would cost about $801 million.