The rusty hulk of the once-gleaming-white 290-yard-long ship, which ran aground on rocks near the Tuscan holiday island of Giglio while carrying out a display manoeuvre, had been resting on a temporary platform since being righted a year ago.
In what has become one of the largest salvage operations in history, air was pumped into 30 large metal boxes, or sponsons, attached around the hull of the 114,500 tonne ship.
The air forced out the water in the sponsons, lifting the vessel off the underwater platform.
Franco Porcellacchia, the engineer in charge of the salvage, said: "The boat is now floating with its sponsons attached. The ship is upright and is not listing either longitudinally or latitudinally. This is extremely positive."
The ship will be further stabilised with chains and cables and tug boats will move it about 30 yards into the harbour, where it will be prepared to be towed within days to Genoa in northern Italy, to be scrapped.
The ship's captain, Francesco Schettino, is on trial accused of manslaughter, causing a shipwreck as he sailed too close to shore to "salute" the port, and abandoning ship. He is fighting the charges.
Paying for the disaster, including breaking up the vessel and repairing the damage to Giglio, is likely to cost the ship's owner and operator Costa Crociere, a unit of Carnival Corp, more than £1 billion, its chief executive said last week.