Ishag and her family were received by Pope Francis at his home for a 30-minute meeting in which he thanked her for her "courageous testament of faith" and her "tenacity", the Vatican said in a statement.
Ishag and her American husband Daniel Wani in turn thanked Francis for the "great support and comfort" they had taken from "the pope's and many other believers' prayers."
The meeting was "a sign of closeness and solidarity for all those who suffer for their faith, in particular Christians who suffer persecution," the Vatican added.
The 77-year-old Argentinian pontiff gave Ishag rosary beads after an "affectionate and warm" chat about her plans in the US, where she is expected to fly with her family in a few days time, Vatican spokesman Federico Lombardi said.
The 27-year-old, her husband and two children arrived at Rome's Ciampino airport at around 9.30am on Thursday morning on a plane provided by the Italian government, Corriere della Sera reported. She was greeted at the airport by Italy's Prime Minister Matteo Renzi, his wife Agnese and Foreign Minister Federica Mogherini.
"Today is a day of celebration", Renzi said.
The mother-of-two was accompanied on the flight by Italy’s Deputy Foreign Minister Lapo Pistelli, who met with Ishag on July 3rd and has been following the case closely.
Pistelli posted a photo on Facebook of the young mother aboard the plane cradling her infant daughter as her toddler son drank from a bottle.
"Mission accomplished," he wrote.
Photo: Facebook/Lapo Pistelli
Pistelli said Pope Francis had been informed of Ishag's arrival, and that a meeting between the pontiff and the Sudanese woman was possible.
Her stay in Italy was organized by the Italian government in collaboration with the Sudanese government. According to Italian news agency Ansa the family will stay in Italy for a few days before flying to New York.
Ishag’s case sparked global outrage in May when she was sentenced to death by hanging for apostasy, the act of renouncing one’s religion.
Ishag, who is married to a US citizen born in what is now South Sudan, was accused of adultery and sentenced to 100 lashings because marriage between a Muslim woman and a Christian man is not recognized under Sudan’s Sharia law which has been in force in 1983.
When she asserted that she was in fact Christian she was then accused of apostasy.
Ishag was born to a Muslim father who abandoned the family, and was raised by her Ethiopian Orthodox Christian mother. The Roman Catholic Archdiocese of Khartoum says Ishaq joined the Catholic church shortly before she married in 2011.
Days after her conviction, the 26-year-old gave birth to a second child, Maya, in prison.
Ishag's conviction was overturned in June, but she was immediately rearrested while trying to leave Sudan using what prosecutors claimed were forged documents.
Two days later, Ishag was released from prison and she and her family took refuge in the US embassy in the Sudanese capital Khartoum.
The case has attracted outrage from world leaders including Italy’s Prime Minister Matteo Renzi, who mentioned Ishag during his speech inaugurating Italy’s six-month presidency of the Council of the European Union.
“If there is no European reaction we are not worthy of calling ourselves Europe,” Renzi said.
Ishag's arrival in the Italian capital follows a European Parliament resolution condemning her “degrading and inhumane treatment” and calling for legal reforms in Sudan.
A spokesperson for the Italian government was not immediately available for comment.