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The operation to raise the 290-metre hulk from underwater platforms next to the Italian island of Giglio where it sank, killing 32 people, should take six or seven days, the group organising the removal said.
The refloating will go ahead if the summer weather remains calm, and then the Concordia, which is around two and a half times the size of the Titanic, is due to be towed to the northern port of Genoa to be scrapped.
The government's Civil Protection Department said that documentation submitted for the refloat was "valid", allowing it "to give the go-ahead for the operation to refloat the Concordia".
The defunct luxury liner is due to depart Giglio on July 21, two and a half years after it struck a reef while performing a display manoeuvre to move close to shore and "salute" the port.
Residents of the tiny island, which depends on tourism, hope this stage in the salvage will repeat the success of a complex "parbuckling" operation which stabilised the wreck last year.
"I am happy they are taking it away because to see a ship like that always there, with the deaths that happened, it gives us the shivers," said ferry worker Italo Arienti.
The ship's captain, Francesco Schettino, is on trial accused of manslaughter, causing a shipwreck and abandoning ship. He is fighting the charges.
Paying for the disaster, including breaking up the vessel and repairing damage to Giglio, is likely to cost the ship's owner and operator Costa Crociere, a unit of Carnival Corp , more than €1.5 billion, its chief executive said last week.