Sergio Girotto, one of the engineers, said the forward lean was "created by the water inside rushing to the bow as the ship was floated", but said that the vessel would right itself as it was raised further over the coming days.
The dirty white liner was then towed around 30 metres away from the coastline with the waterline in the part that had been submerged clearly visible.
Divers who had worked to prepare the operation through the night could be seen returning to port on a dinghy, cheering.
The luxury liner sank after hitting rocks on January 13, 2012 in a tragedy which left 32 people dead.
South African salvage master Nick Sloane had boarded the ship at dawn, telling journalists he was "nervous" about this stage of the operation which could see the battered ship break up.
"Today we'll see whether our calculations were correct," the sandy-haired mariner said, before heading to oversee the operation from a control room on board the Costa Concordia itself.
The ship - twice as big as the Titanic - will be refloated over a six-to-seven day period then towed away for scrapping to a port in Genoa in northern Italy.
On Tuesday and Wednesday, the last tanks or "sponsons" on the 290-metre Concordia will be lowered into position and the final steel chains attached underneath the vessel to support it.
"The risks are that the ship could bend as it is raised, or the chains underneath it could snap," Sloane told AFP before the operation.
"If disaster strikes we will evacuate through emergency escapes on the bow and stern," he said.
The main refloating operation is set to take place between Thursday and Saturday, when air will be pumped into the tanks to raise the ship the remaining 10 or so metres.
"It's an unprecedented operation and, as with anything being done for the first time, there are risks. But we are confident," Porcellacchia said.
The Concordia crashed off Giglio, forcing many of its 4229 passengers and crew from 70 countries to jump into the sea as lifeboat pulleys failed.
The ship's captain Francesco Schettino is on trial for manslaughter, causing a shipwreck, and abandoning the vessel before all passengers had evacuated.
Costa Concordia
The ship
*The Costa Concordia is 290m long - the equivalent of nearly three football fields.
*Biggest Italian passenger ship ever - two and a half times as heavy as the Titanic.
*Four swimming pools and largest spa centre on any cruise ship.
*Nine-deck-high, glass-domed lobby and an array of entertainment and shopping facilities.
The wreck
*The ship rolled onto its side when it sank and had to be pulled upright in a delicate operation last September.
*It's resting on six purpose-built steel platforms - at a depth of about 31m.
*30 giant steel tanks or "sponsons" have been welded onto the ship and will work as a pneumatic system to raise it.
*Pressured air will be pumped into the sponsons, expelling the water inside to float the ship.
*Ten boats will accompany the Concordia to Genoa, carrying emergency equipment to be used in case of toxic leaks from the ship.
*500 salvage workers from 26 countries, including 120 divers, have taken part in the salvage and used 30,000 tonnes of steel.
*Ship owner Costa Crociere estimates the cost of the salvage so far at 1 billion ($1.5 billion).
- additional reporting AFP
