The Alan Kurdi and Ocean Viking rescue ships were given permission to dock in the Sicilian ports of Messina and Pozzallo on Wednesday morning and safely offload their 121 passengers.
Both ships rescued migrants from the Mediterranean on November 28 and had been waiting for approval to enter a safe port.
“The European Commission has started the procedure of distributing the 61 migrants on the Alan Kurdi and the 60 aboard the Ocean Viking,” the ministry said in a statement.
“Some European countries, including Germany and France, have offered to accommodate some of these migrants.”
The ships were authorised to dock thanks to a temporary distribution system agreed in September with France, Germany, Italy and Malta.
The deal was meant to end the long, drawn-out negotiations that have seen vulnerable asylum-seekers including babies stranded at sea, sometimes for weeks.
Both rescues took place in the Libyan search and rescue zone.
The Alan Kurdi had rescued 84 people in total, including three small children and three newborns and 21 women.
One of the women rescued was pulled unconscious from the sea, while another is pregnant.
One of the newborns was in a critical condition, having had no water or milk for two days.
Twenty-three people had been evacuated for medical reasons in the following days.
Meanwhile, the crew on the Ocean Viking reported that of the 60 people they rescued, there were 19 minors, including a three-month-old baby and his three-year-old brother.
Seventeen of the minors were reportedly unaccompanied.