Meriam Ibrahim Tehya Ishag, who met Pope Francis during her eight-day stopover in Italy, took an American Airlines flight for Philadelphia.
The 26-year-old, her two infant children and American husband Daniel Wani are expected to travel on Friday to New Hampshire, where Wani's brother lives.
During the family's stay in Rome they were put up by the interior ministry, under police protection, Antonella Napoli, head of the Italians for Darfour association, told Huffington Post Italy.
Between visiting the Colosseum, shopping and attending mass in Saint Peter's Basilica, the family "learned how to live again," she said.
The White House last week said it was delighted at Ishag's release and looked forward to welcoming her to the United States.
A global outcry erupted in May after Ishag was sentenced under sharia law to hang for apostasy. Days after her conviction, she gave birth to her daughter 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 because of mounting death threats.
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.
She was convicted under Islamic sharia law that has been in force in Sudan since 1983, and that says Muslim conversion to another faith is punishable by death.
The court had also sentenced her to 100 lashings because under sharia law it considered her union with her non-Muslim husband to be adultery.
Ishag's case raised questions of religious freedom in mostly-Muslim Sudan and sparked vocal protests from Western governments and human rights groups.
The case has re-focused attention on a country which has slipped from the international spotlight but where war continues with millions of people in need of humanitarian aid.