“Disembarking will begin in the coming hours,” Conte told reporters on Wednesday.
France, Germany, Malta, Portugal, Romania and Luxembourg have agreed to accept some of the migrants who were rescued by the Dutch-flagged Sea-Watch 3 on January 19.
The vessel had been stranded in Sicilian waters for over a week after Italy and other European nations refused to let it dock.
Sea-Watch on Friday filed an urgent case at the European Court of Human Rights (ECHR) against Italy for refusing to allow its ship to dock and the mainly sub-Saharan migrants, including 15 minors, to disembark.
The ECHR on Tuesday ordered Italy to provide medical assistance, food and drinks to the migrants aboard the boat.
Italian Interior Minister Matteo Salvini last week accused the boat of putting the migrants’ lives at risk by sailing straight for Italy rather than docking at closer ports in Libya or Tunisia.
Sea-Watch claimed it tried but failed to get a response from Tripoli or Tunis.
People in the Sicilian city of Syracuse, less than a kilometre from where the vessel was taking shelter offshore, offered assistance once the migrants disembark.
A group of hotel and B&B owners in Syracuse said they’d take in all 47 migrants and help integrate them at their own cost, from sending them to Italian lessons to providing employment opportunities.
This is the second time in a month Sea-Watch 3 has been stranded at sea with migrants on board.
The last stand-off ended after 19 days with an agreement among eight EU countries, including Italy, to each take in some of the migrants.
Since Italy closed its docks to private rescue boats last year, Sea-Watch 3 is the only ship working to rescue migrants in the central Mediterranean.