The Blue Sky M had apparently been abandoned by its crew and at one point seemed to be heading directly towards the Italian coast on autopilot.
Reports suggest Syrians and Kurds are among those aboard the ship.
Photos posted by the local Italian Red Cross show the ship in port with people crowding a deck.
Ambulance crews stood waiting as the ship docked in the early hours of New Year's Eve amid unconfirmed reports that people on the ship were suffering frostbite.An eyewitness in Gallipoli, local man Gilberto Busti, told the BBC World Service he had seen hundreds of people - who he thought could be Syrian and Kurdish refugees - disembarking from the vessel.
Mr Busti said he had heard reports that some of those on board might be dead.
"I saw the ship arrive and the coaches that carried off the migrants," he said.
"I saw the police and the Red Cross that set up the tents. I have a friend in civil protection who told me that there were about 800 to 900 people inside the ship. We can't confirm that there are dead people inside but my friend told me that there were about four or five dead people."
Italy has had to deal with a massive surge in migrants - many of them from the Middle East and the Horn of Africa - setting off on boats with hopes of reaching Europe.
The most common sea route for the clandestine voyages has been from Libya but this ship is said to have started in Turkey. It is also unusual to find a vessel of this size carrying migrants.
People traffickers who organise the crossings often abandon the vessels at sea to avoid arrest.
The UN High Commissioner for Refugees, Antonio Guterres, has warned that his agency will face enormous shortages in 2015 as it struggles to deal with what he called a staggering escalation of humanitarian needs across the globe.
Mr Guterres said his organisation might not be able to deliver even the minimum level of assistance needed for many refugees to survive.
'Disaster averted'
The Blue Sky is listed as a general cargo ship, flying under a Moldovan flag.
Italian coast guard spokesman Filippo Marini was quoted by AP news agency as saying the Italians had averted a disaster by interrupting the programmed route that would have had the ship crash into the shore.Greek officials were first alerted to the ship when it was near Corfu.
A man aboard is reported to have asked for food, water and blankets. The distress call to Greek emergency services prompted the navy to send a helicopter and a warship.
The Greek authorities said no-one aboard the vessel was in danger.
The Blue Sky M was reportedly heading for the port of Rijeka in Croatia from Turkey.
According to tracking website MarineTraffic, the ship abruptly changed direction south of Othonoi on Tuesday morning, heading west towards Italy.
Weather conditions in the Ionian sea have been poor for several days, hampering the rescue of those on board the Norman Atlantic ferry which caught fire in the area, killing at least 10 people.
