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The wrecked Italian cruise ship, the Costa Concordia, is being towed to the port of Genoa for scrapping after a two-year salvage operation.
Its removal is one of the biggest ever maritime salvage operations.
The Concordia struck a reef off the Italian island of Giglio in January 2012 and capsized, killing 32 people.
Captain Francesco Schettino has denied charges of multiple manslaughter and abandoning ship, which could see him jailed for up to 20 years.
The Costa Concordia was re-floated nine days ago and is being kept above the surface by giant buoyancy chambers.
More than a dozen vessels will help to tow the ship.
Costa Concordia Giglio wreck removal aerial view from drone
The wreck was hauled upright in September last year but was still partially submerged, resting on six steel platforms.
Sirens on nearby boats wailed and bells on Giglio tolled just before two tugboats pulled the vessel away.
Italian civil protection service head Franco Gabrielli told the Reuters news agency that "victory" could only be declared when the ship was in sight of the port of Genoa.
The cruise ship is being towed to Genoa at two knots, almost at walking pace, with an escort of more than a dozen tug boats.
The journey, which is expected to take four days, began shortly before 09:00 local time (07:00 GMT).
Senior salvage master Nick Sloane said early on Wednesday that everything was going according to plan.
However, French ecology minister Segolene Royal has said she will monitor the ship's movement from Corsica. Residents on the island fear that any oil leak from the cruise ship could cause significant environmental damage.
The Concordia is set to sail 25km (15 miles) from Corsica and close to the islands of Elba and Capraia before its expected arrival in Genoa late on Saturday.
A survivor of the tragedy told Reuters that initially he saw the area where the ship sunk as "a place where I saw tragedy strike", but over time his view had changed because it was a miracle that 4,000 people were saved.
Investigators are still looking for the body of Indian waiter Russel Rebello, whose body is the only one not to have been found.
The Costa Concordia's owners, Costa Crociere, estimate the operation to remove the wreck from the reef and tow it for scrapping will cost 1.5bn euros (£1.2bn; $2bn) in total.
- GeoGarage blog : Delicate operation to refloat Costa Concordia begins in Italy