"If weather conditions allow, the operation will start at 6.00am on 16th September," Franco Gabrielli, head of the civil protection agency, which is overseeing the operation, said on Thursday.
"This is an operation that has never been attempted before," Gabrielli said in a press conference.
Once the rusting luxury liner is upright, it will be towed away for scrapping.
The 114,500-ton ship has been lying on its side just off the tiny Tuscan island of Giglio ever since it hit rocks and keeled over with 4,229 people from 70 countries on board in January 2012.
The night-time disaster claimed 32 lives.
Using giant cement sacks and a custom-made metal platform, the salvage operation has so far secured the rusting hulk, which was threatening to slip off an underwater rock shelf into deeper waters.
The plan is to drag it up using cables and pulleys - a complex and delicate operation since the hull of the ship is badly damaged 20 months after the crash.
Italy's civil protection agency said the official go-ahead would be given only on Sunday afternoon.
The operation is expected to take between 10 and 12 hours and officials have said they will block all maritime traffic in the area until it is over.
"The size of the ship and its location make this the most challenging operation I've ever been involved in," said Nick Sloane, the chief salvage operator.
Sloane said he was prepared for the hull to buckle as it is being raised and emphasized the operation had to be carried out this month because of its weakened condition and the prospect of winter storms.
Gabrielli ruled out the possibility of the hull splitting in two, but said they were prepared for "everything that could go wrong...cables snapping, structures collapsing...a wave sent rushing back onto people on the portside".
Sloane explained the ship would initially be dragged up with ropes for four or five hours before gravity takes over and it begins to right itself on its own, with giant metal tanks fixed on the side currently exposed acting as brakes to prevent it from flipping over.
Salvage workers have already removed the fuel from the ship in order to prevent an environmental disaster in the area, one of Europe's biggest marine sanctuaries.
But environmentalists have warned of the potential danger of toxic chemicals from the ship pouring into the sea as it is rolled over in what is known in shipping terminology as a "parbuckling".
Gabrielli admitted there would be some spillage.
The island's economy depends hugely on tourism and locals say the presence of the wreck has brought down visitor numbers in the past two summers.
Tanks or "sponsons" have been welded onto one side of the ship and the plan is to fix more onto the side that is now underwater once it has been raised.
The tanks would then act as giant flotation devices to allow the 290-metre vessel to be towed away to be dismantled, probably early next year.
The salvage operation is the biggest ever attempted for a passenger ship and has been delayed repeatedly.
The project is being financed by insurance for ship owner Costa Crociere, Europe's biggest cruise operator.
Officials on Thursday said the cost was "€600 million and rising" and insurance companies have warned that it could rise as high as €825 million in total.
Two bodies - that of an Indian crew member and Italian passenger - have yet to be recovered and are believed to be trapped under the ship.
Gabrielli said any attempt to recover remains would have to wait until the righting operation is complete for safety reasons.
Four crew members and the head of Costa Crociere's crisis unit were handed short prison sentences after negotiating plea bargains over their role in the crash.
The ship's captain, Francesco Schettino, is currently on trial accused of manslaughter and abandoning the ship before all its passengers had been evacuated.