The rusting prow of the once-gleaming white luxury liner has emerged fully from the water for the first time.
The ship should have been ready to be towed on Sunday but the departure was pushed back until Monday due to forecasts of rough seas.
The 114,500-tonne Concordia has been slowly lifted from the sea floor since last week when salvagers began pumping air into 30 large metal boxes around the hull.
A convoy of 14 vessels planned to tow the Concordia to a port near Genoa, where it will be broken up for scrap, completing one of the biggest maritime salvage operations in history.
The president of the French Concordia survivors' group, Anne Decre, who is on the island of Giglio, said the departure of the ship would be an important symbolic moment for those who were aboard the night of the shipwreck.
"It gives us the opportunity to try and collect ourselves and move forward," she said, adding that the liner will take the same route to Genoa it should have taken more than two years ago to complete its ill-fated cruise. "We hope we will also be able to return to our route."
The ship's captain, Francesco Schettino, is on trial on charges of manslaughter.