Some 137 migrants left the Diciotti early on Sunday, stepping on to the dock at Catania, Sicily, where police photographed them for ID checks, a requirement for asylum seekers.
Italy's populist government had not let them leave the ship earlier, demanding that other European Union countries take them.
Only Ireland did, pledging to take 20.
Non-EU Albania will take 20, while Italian Catholic bishops said they would care for about 100.
On August 16, the Diciotti's crew rescued 190 migrants, most from Eritrea, from a smuggling boat.
The others, including minors and ailing migrants, were allowed off earlier.
Italy has threatened economic reprisals against the EU for not helping it enough with migrants.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.
