The migrants were picked up by the Marella Discovery, an 11-deck luxury liner equipped with swimming pools, a casino and a theater.
The migrants' boat was found in distress on Saturday evening, some 74 kilometers (40 nautical miles) off Greece's Peloponnese peninsula.
Read more: Alleged migrant smugglers arrested on Greek islands
Of the 111 people on board, 33 were children.
The coast guard did not say which countries the migrants were from or where their boat departed.
Migrants taken to Greek portThe passengers were taken to the Greek port of Kalamata.
Two of the migrant boat's operators were arrested.
Several times a week, boatloads of people — many of them from Africa — attempt to cross the Mediterranean Sea for a better life in Europe.
Greece, Italy and Spain have borne the brunt of the influx of newcomers over the past decade, many of whom are picked up by migrant rescue ships operated by European charities.
A failure by European Union states to agree an effective disembarkation procedure has prompted Italy's populist government to ban several migrant ships from docking at the country's ports.
Read more: Refugees sent to Libya under EU deal face 'catastrophic' conditions
Migrant crossings fallingAlthough the number of migrants attempting the perilous journey has fallen from 362,000 in 2016 to 116,000 in 2018, an average of six migrants die every day in the Mediterranean, the UN High Commissioner for Refugees reports.
Already this year, at least 426 men, women and children have died during the crossing, according to the French medical charity Doctors Without Borders (MSF).
MSF and the NGO SOS Mediterranee on Sunday announced they would resume migrant rescues with the 69-meter Ocean Viking ship.
The two groups' previous ship, Aquarius, discontinued its work in December following hostility from several European governments.
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