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'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.
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.