The sound of ship horns sounded across the water in celebration, mixing with applause and cheers in the port in a climax to the 19-hour operation.
The 290-metre, 114,500-ton vessel - longer than the Titanic and more than twice as heavy - rose from the sea like a ghost ship.
The side of the giant ship that had been underwater was rusty and brown 20 months on from the Janaury 13th 2012 tragedy, contrasting with the brilliant white on the exposed side.
"The parbuckling operation has been completed," said Franco Gabrielli, head of the civil protection agency and project overseer, using the technical term for the rotation.
Gabrielli said the newly exposed side would require "major repairs" and removal of the ship for scrapping is planned only for the spring of next year at the earliest.
Local residents and survivors spoke of an eerie feeling as the ship rose, saying it reminded them of the way the ship looked on the night of the tragedy that claimed 32 lives.
"Seeing it re-emerge is emotional for me," said Luciano Castro, a survivor who travelled to the picturesque island to witness the salvage.
"I could not miss it. That ship could have been my end and instead I am here to tell the story," he said.
The salvage is the biggest for a passenger ship ever undertaken and the position of the hulk posed unique challenges to the 500-person international salvage team.
They also had to take special care since Giglio is in the heart of one of Europe's biggest marine sanctuaries.
The ship was dragged up with 36 cables across the hull and tanks the size of 11-storey buildings welded on the side of the ship which were filled with water to act as ballast.
The project has so far cost €600 million and insurers, who are picking up the bill, estimate it could run to €825 million once it is completed.
The man who gave the orders from a control room on a barge next to the ship was Nick Sloane, a South African with experience on some of the world's biggest shipwrecks.
"I'm relieved. It was a bit of a rollercoaster," a smiling Sloane said as he was mobbed by dozens of journalists and well-wishers in the port before a celebratory drink.
"The scale of it was something we've never seen before," he said.
Admiral Stefano Tortora, who took part in the operation, said: "The condition it's in is really shocking. It is disturbing because you are looking at a tragedy."
Giglio islanders said they were happy at the prospect of the ship finally being refloated and towed away.
"All the inhabitants are hoping and waiting," said Giovanna Rum, owner of a maritime clothing shop on the island.
The Costa Concordia struck rocks just off Giglio after veering sharply towards the island in a bravado sail-by allegedly ordered by its captain, Francesco Schettino.
Dubbed "Captain Coward" and "Italy's most hated man" in the tabloids for apparently abandoning ship while passengers were still on board, Schettino is currently on trial.
Four crew members and the head of ship owner Costa Crociere's crisis unit have already been handed short prison sentences for their roles in the crash.
The ship had 4,229 people from 70 countries on board.
It keeled over within sight of Giglio's port but the order to abandon the vessel came more than an hour later.
After several lifeboats failed to function, hundreds were forced to either jump into the water and swim ashore or lower themselves along the exposed hull to waiting boats.
The bodies of Indian waiter Russell Rebello and Italian passenger Maria Grazia Trecarichi were never recovered.
Their loved ones were expected on Giglio later on Tuesday ahead of a new search due to be launched for the corpses.
Elio Vincenzi, Trecarichi's husband, said: "I am filled with hope. I am still hoping to find my wife. This is a tense wait for me and for my daughter."