The nurses were flown back on Saturday morning on a special Air India flight.
They had been stranded while working at a hospital in the northern city of Tikrit for more than a week.
Sunni rebels led by militant group Isis have occupied large swathes of northern and western Iraq.
They have declared a large region straddling Iraq and Syria a caliphate or Islamic state.
About 10,000 Indians are reported to be working in Iraq. Scores of them have returned to India since fighting began.
"We are very happy [to be freed]," Marina Jose, one of the nurses released by the militants told NDTV. "We never thought we would come out because the situation was very bad."
She said that the militants had for the most part treated them well.
At the airport: Imran Qureshi, BBC News, Kochi
The nurses received a tumultuous welcome, led by their families and the chief minister of the southern state of Kerala, Oomen Chandy. Every political party was represented.
The nurses gave differing accounts of how they had been treated. One nurse, Shermin Varghese, told the BBC the militants in Tikrit had said they were being taken to an airport. Another, Marina Jose, said they had been told only that they were heading to Mosul.
They said they had burst into tears when the militants showed them their bombs and ammunition on the bus. But both of them said they had not been mistreated.
The exact circumstances of their release are unclear - they are reported to have been pressured into boarding buses and leaving the hospital by jihadist fighters from the Islamic State in Iraq and the Levant (Isis).
They were reportedly then taken to Mosul before being freed.
The specially-chartered flight was also carrying about 100 other Indians leaving Iraq.
Tikrit is among a number of towns and cities seized by jihadist-led Sunni rebels in recent weeks.
Some of the nurses told the BBC by phone a few days ago that fighting had reached the hospital compound and there had been several explosions close to where they had been hiding.
A group of 46 Indian nurses freed by Isis militants after being trapped in Iraq has arrived home in the southern city of Kochi to be greeted by rapturous friends and relatives.