Salvage crews refloated the ship last week so they can move it from its resting place off Giglio Island to the Italian port of Genoa to be dismantled.
On Wednesday morning, the rusting hulk set off into open waters under tow.
Attached to its sides are the huge steel hollow boxes, or sponsons, that were pumped full of compressed air to give the ship buoyancy.
It's been more than 2½ years since the ship ran aground off Giglio Island with more than 4,200 passengers aboard, killing 32 people in a disaster that drew global attention.
The vessel will be towed - slowly and carefully - approximately 150 miles to Genoa, where it will be broken up. A convoy of 17 boats will travel along with it.
The ship is expected to arrive in Genoa on Sunday. It'll take about two years to dismantle the massive cruise liner.
Environmental concerns prompted the decision to undertake the expensive and difficult process of refloating the Costa Concordia rather than taking it apart on site.
Since the wreck two years ago, 24 metric tons of debris - including furniture, dishes, food, personal effects and ship parts - have been recovered from the seabed.
The Costa Concordia is the largest salvage ever attempted - and the most expensive, at a cost of $1.5 billion so far.