They are hopeful they can rotate the liner upright and eventually tow it away.
Never before has such a big cruise ship been righted, and the crippled Concordia did not move for the first three hours after the operation began. After 6000 tons of force were applied using pulleys and counterweights, it moved from the reef.
Engineer Sergio Girotto said the cameras did not reveal any sign of the two bodies that were never recovered from among the 32 who died when the Concordia slammed into a reef and capsized after the ship's captain steered it too close to Giglio Island.
Images transmitted by robotic diving vehicles indicated that the submerged side of the hull had suffered "great deformation" from all its time on the granite seabed, Mr Girotto said.
The initial operation to lift the Concordia from the reef moved the ship just three degrees toward vertical, leaving the vessel 62 degrees shy of being pulled upright. While a seemingly small shift, the movement was significant enough to be visible: A few feet of slime-covered hull that had been underwater became visible.
The entire rotation was expected to last as long as 12 hours.
So far, "rotation has gone according to predictions," and no appreciable pollution from the ship has spewed out, said Franco Gabrielli, chief of Italy's Civil Protection agency, which is overseeing the operation.
Giglio is part of a Tuscan archipelago in a marine sanctuary where dolphins and fish are plentiful.
The operation, known as parbuckling, is a proven method to raise capsized vessels.
The 1000-foot, 115,000-ton Concordia is the largest cruise ship ever to capsize.
The operation involves engineers using remote controls to guide pulleys, counterweights and huge chains looped under the Concordia's hull to nudge it free from its rocky seabed and rotate it upright.
During the rotation process, a series of tanks fixed on the exposed side of the hull will be filled with water to help pull it down.
Once the ship is upright, engineers hope to attach tanks filled with water on the other side to balance the ship, anchor it and stabilise it during the winter months.
When it comes time to tow the ship in spring, the tanks will gradually be emptied of the water so the ship becomes buoyant enough to float off the seabed.
The Concordia's captain is on trial for manslaughter, causing a shipwreck and abandoning the ship during the chaotic and delayed evacuation. Francesco Schettino claims the reef was not on the nautical charts for the liner's week-long cruise.