The wrecked cruise ship’s removal was one of the biggest ever maritime salvage operations.
Costa 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.
Italian PM Matteo Renzi is expected in Genoa in the afternoon to see the end of the complex docking procedure, which is expected to take several hours.
“The operation to recover the Concordia was not easy. Italy carried it out, the Italy that, when it sets out to, is capable of doing anything, even of surprising us,” Matteo Renzi said.
Antonio Benvenuti, the head of Genoa’s harbor workers’ union, told AP that there was no “precise schedule” for each stage of dealing with the wreck.
Tests will be carried out first to monitor for potential pollution problems, Antonio Benvenuti said, before the first stage of the operation would begin, reducing the weight of the ship in order to lift it.
The Costa Concordia was re-floated nine days ago and was kept above the surface by giant buoyancy chambers. More than a dozen vessels helped to tow the ship after it was pulled away from Giglio on Wednesday.
The wreck was hauled upright in September last year but was still partially submerged, resting on six steel platforms.
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 1.5 billion euros ($2 billion) in total.
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