The wrecked cruise ship – the target of one of the biggest maritime salvage operations in history – is now floating about 3ft off the platform.
In all, the refloating operation is expected to take six or seven days.
The cruise liner will then be towed to its home port, Genoa, where it will be scrapped.
Costa Concordia struck a reef off the Italian island of Giglio in January 2012 and capsized, killing 32 people.
Workers are slowly lifting the vessel by pumping air into tanks attached to the ship. The wreck was hauled upright in September but was still partially submerged, resting on six steel platforms.
Salvage workers cheered with delight as they returned to Giglio’s port.
“The ship is upright and is not listing. This is extremely positive,” the engineer in charge of the salvage, Franco Porcellacchia, told a news conference.
A search for the remains of Indian waiter Russel Rebello, whose body was not recovered from the wreck, will be carried out after the vessel is moved.
The Costa Concordia’s owners, Costa Crociere, estimate the operation to remove the wreck from the reef and tow it for scrapping will cost 1.5 billion euros ($2 billion) in total.
An engineer with Costa Crociere described the salvage efforts as “unprecedented”.
“As with anything being done for the first time, there are risks. But we are confident,” Franco Porcellacchia said.
Hundreds of divers and engineers have been involved in operations to salvage the Concordia, which is twice the size of the Titanic.
Towing the ship to Genoa – about 200 nautical miles away – is due to begin on July 21 and take about five days.
“The operation began well but it will be completed only when we have finished the transport to Genoa,” Italian Environment Minister Gian Luca Galletti told reporters on Monday.
Costa Concordia’s captain Francesco Schettino is on trial for manslaughter and abandoning ship, charges he denies.
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