The Italian navy vessel arrived after a 36-hour voyage carrying 16 men from Bangladesh and Egypt.
They will be settled in prefabricated housing while their asylum requests are processed.
Italy's two processing centres in Albania, surrounded by high walls and security cameras, are at Camp Gjader, 20 kilometres (12 miles) from the port.
They will be operated under Italian law, with Italian security and staff, and judges hearing cases by video from Rome.
If an applicant's asylum request is refused, cells have been set up on site.
Human rights groups have questioned whether there will be enough protection for asylum seekers. They have expressed doubts, too, as to whether it complies with international law.
But Italian Prime Minister Giorgia Meloni brushed aside criticism in comments on Tuesday.
"It is a new, courageous, unprecedented path, but one that perfectly reflects the European spirit and has everything it takes to be followed also with other non-EU nations," she said.
The arrangement between the two countries is a European first, which other leaders in the region are watching closely.
The project was agreed in a November 2023 deal between Italy and Albania. Set to last five years, it will cost Italy an estimated 160 million euros a year.
The centres will have a capacity of 1,000 initially growing to 3,000 in the long term.
Its critics say that given such numbers, the scheme cannot be justified.
"Over the last three years, more than 1,600 migrants have landed in Italy," migration researcher Matteo Villa of Datalab Europe posted on X. "An Italian navy vessels is taking 16 to Albania.
"I don't think I need to add anything else."
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