The so-called parbuckling operation to right the wrecked liner involved lifting it off a rock shelf and rotating it so it would sit upright on an underwater platform, the Italian news agency ANSA reported.
The Costa Concordia was carrying about 4,000 people when it capsized in January 2012 near Giglio Island, killing 32 people. Two remain missing. The ship had been partially submerged since.
"It was a perfect operation, I'd say," said Franco Porcellacchia, technical team leader for the ship's owners, Costa Cruises.
Porcellacchia said there wasn't evidence of any environmental impact, The New York Times reported.
The operation started Monday after a storm delayed its start by three hours.
Authorities said the top priority now was to find the bodies of the two victims that have not been recovered.
Once stabilized upright, the Costa Concordia will be towed and sold for scrap sometime early next year, ANSA said.
Costa Cruises, which owns the Costa Concordia, said last week the salvage operation cost about $801 million so far, and the price tag was rising.
As the Concordia was righted, ships' horns blared to celebrate and some of the island's residents hugged salvage workers as they came ashore, the Times reported. The operation was broadcast live on television and the Internet.
"This was an important, visible step," Franco Gabrielli, head of Italy's Civil Protection Agency, told reporters.
The Costa Concordia had just begun a Mediterranean cruise when it struck the reef off the island of Giglio. Investigators say the captain, Francesco Schettino, who is awaiting trial, deviated from the course and went too close to the island.