Last week, authorities in Tuscany who wanted the lucrative dismantling contract to go to the local port of Piombino had vetoed decisions in favour of Genoa by a technical panel, which was forced to delegate the issue to the national government.
"#Concordia is going to Genoa," Environment Minister Gian Luca Galletti tweeted after a cabinet meeting in Rome.
"An Italian solution rewards our efforts. Now we will be on the lookout for maximum environmental protection."
Costa Crociere, a subsidiary of US group Carnival, which owns the Concordia, had already picked Genoa as its preferred location.
Chief executive officer Michael Thamm welcomed the government's go-ahead. "We are close to the finish line. We are two weeks away from possible refloating," he said.
A location in Turkey was a cheaper but riskier option for the dismantling, because of the much longer trip to reach the destination. Refloating and moving the Concordia - a 300m, 114 000-ton vessel - out of Giglio's shoreline is a major engineering effort, during which there is a risk of toxic substances being released.
The procedure is expected to be completed by the end of July.
The Concordia hit a reef and partly capsized on 13 January 2012, after being steered dangerously close to Giglio, in an alleged stunt by captain Francesco Schettino. Thirty-two of the 4 229 people onboard were killed.