There was global condemnation when she was sentenced to hang for apostasy by a Sudanese court.
Mrs Ibrahim's father is Muslim so according to Sudan's version of Islamic law she is also Muslim and cannot convert.
She was raised by her Christian mother and says she has never been Muslim.
Welcoming her at the airport, Italy's Prime Minister Matteo Renzi said: "Today is a day of celebration."
Mrs Ibrahim met Pope Francis at his Santa Marta residence at the Vatican soon after her arrival.
|Meriam, Maya and Pope Francis|
The meeting, which lasted around half an hour, was intended to show "closeness and solidarity for all those who suffer for their faith," he added.
The BBC's Alan Johnston in Rome says there was no prior indication of Italy's involvement in the case. That's simply not true, I have mentioned it twice myself so there must have been. In fact, this from the Italian government:
Mariam Yehya Ibrahim, the Sudanese Christian woman sentenced to death in Sudan for apostasy but subsequently pardoned, arrived in Rome on Thursday, the Italian Foreign Ministry said.
Ibrahim “will remain in Italy for a short time and then will travel on to the United States,” the ministry said. …
[Deputy Minister for Foreign Affairs Lapo] Pistelli said Italy had become involved in the case because, as a Catholic country, it was very moved by Ibrahim’s story and wanted to help.
Italy has good relations with Khartoum and offered to help the U.S. Embassy there to speed up the process of getting U.S. passports for Ibrahim and her family to leave the country, the minister said.
Pistelli said he had traveled to Sudan two weeks ago to start the process but it was not finalized until Wednesday night.
He posted an image to his Facebook page of himself with Ibrahim and the two infants, apparently taken on board the plane shortly before their arrival in Rome. “Mission accomplished,” he wrote.
Lapo Pistelli, Italy's vice-minister for foreign affairs, accompanied her on the flight from Khartoum and posted a photo of himself with Mrs Ibrahim and her children on his Facebook account as they were about to land in Rome.
"Mission accomplished," he wrote.
A senior Sudanese official told Reuters news agency that the government in Khartoum had approved her departure in advance.
Mrs Ibrahim's lawyer Mohamed Mostafa Nour told BBC Focus on Africa that she travelled on a Sudanese passport she received at the last minute.
"She is unhappy to leave Sudan. She loves Sudan very much. It's the country she was born and grew up in," he said.
|Meriam's husband Daniel Wani in Rome airport|
Mrs Ibrahim's husband, Daniel Wani, also a Christian, is from South Sudan and has US nationality.
Their daughter Maya was born in prison in May, shortly after Mrs Ibrahim was sentenced to hang for apostasy - renouncing one's faith.
Under intense international pressure, her conviction was quashed and she was freed in June.
She was given South Sudanese travel documents but was arrested at Khartoum airport, with Sudanese officials saying the travel documents were fake.
These new charges meant she was not allowed to leave the country but she was released into the custody of the US embassy in Khartoum.
Last week, her father's family filed a lawsuit trying to have her marriage annulled, on the basis that a Muslim woman is not allowed to marry a non-Muslim.
Thank God she is finally out of the asylum called Sudan. Lord keep her and her family safe from the lunatics who might try to kill her.