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Mariam Yahya Ibrahim, whose sentence and detention triggered international outrage, walked off the aircraft cradling her baby and was greeted by Italian Prime Minister Matteo Renzi.
Soon afterwards, Ibrahim, her husband and two children had a private meeting with Pope Francis in the Vatican. "The Pope thanked her for her witness to faith," Vatican spokesman Father Federico Lombardi said.
The meeting, which lasted around half an hour, was intended as a "sign of closeness and solidarity for all those who suffer for their faith," he added.
There were no details on what led up to the 27-year-old woman's departure after a month in limbo in Khartoum, but a senior Sudanese official said it had been cleared by the government.
"The authorities did not prevent her departure that was known and approved in advance," the senior official told Reuters, speaking on condition of anonymity.
U.S. national security adviser Susan Rice said Ibrahim's departure was "a testament to her unyielding faith and the support she received from friends and allies," including the U.S. and Italian governments.
The U.S. envoy to the United Nations, Samantha Power, said Ibrahim had become "a symbol for all who suffer for their faith around the world."
While expressing relief Ibrahim was able to leave Sudan, Power called on Khartoum "to repeal the laws that put her in jail in the first place."
"Sudan must respect the universal human rights - including the right to freedom of religion - of all of its citizens, and the United States will continue to fight for all who are denied these fundamental freedoms, in Sudan and around the world," Power said in a statement.
Ibrahim was accompanied on the plane by Italy's vice minister for foreign affairs, Lapo Pistelli. He told journalists at Ciampino airport that Italy had been in "constant dialogue" with Sudan, but did not give any more details on Rome's role in securing her exit.
He published a photograph on his Facebook page of himself with Ibrahim and her two children on the plane with the caption: "A couple of minutes away from Rome. Mission accomplished."
Ibrahim was sentenced to death in May on charges of converting from Islam to Christianity and marrying a Christian South Sudanese-American.
IN GOOD HEALTH
Her conviction was quashed last month, but Sudan's government accused her of trying to leave the country with falsified papers, preventing her departure for the United States with her husband and two children.
She was initially detained, then released and moved into the U.S. Embassy in Khartoum.
Pistelli told reporters at the airport that the family was in good health and would stay in Italy for a few days before leaving for the United States.
The minister, who carried one of Ibrahim's young children off the plane, said he expected her to have "some important meetings" during her time in Italy.
Ibrahim says she was born and raised as a Christian by an Ethiopian family in Sudan and later abducted by a Sudanese Muslim family.
The Muslim family denies that and filed a lawsuit to have her marriage annulled last week in a new attempt to stop her leaving the country. That case was later dropped.
Renzi mentioned Ibrahim's case in his speech to inaugurate Italy's six-month European Union presidency earlier this month.
"If there is no European reaction we cannot feel worthy to call ourselves 'Europe'," Renzi said.
Apostasy is punishable by death in many countries' interpretation of Islamic law