The 40-year-old, from Hampstead, north London, has now travelled to see her family in Damavand, north east of Tehran.
The Free Nazanin campaign, which is run by Ratcliffe, tweeted a series of pictures of Zaghari-Ratcliffe embracing her four-year-old daughter, Gabriella.
'Initially the release is for three days - her lawyer is hopeful this can be extended.
Richard Ratcliffe, the husband of Nazanin Zaghari-Ratcliffe, said that the she was granted temporary leave from Evin Prison in Tehran on Thursday morning.
"This was a very happy surprise after a number of false dawns recently, which had been increasingly unsettling".
She became eligible for release according to Iranian law in November 2017.
Mr Ratcliffe said: "It's great for Nazanin today to be seeing all the news attention and realise how much care there is out there".
A British-Iranian mother who is serving a prison sentence in Iran has been temporarily released.
Former Indian Prime Minister Atal Bihari Vajpayee Dies
Those who enquired after included prime minister Narendra Modi, union ministers and Bharatiya Janata Party (BJP) stalwarts. Vajpayee was the prime minister between 1998 and 2004 when the National Democratic Alliance government was in power.
Hunt told reporters at United Nations headquarters in NY that she "is innocent" and "every day that she is in prison is a reminder to the whole world of a gross injustice".
She was convicted of plotting to overthrow Iran's clerical establishment, a charge denied by her family and the Foundation, a charity organization that is independent of Thomson Reuters and operates independently of Reuters News. Johnson later distanced himself from his remarks.
Zaghari-Ratcliffe was warned not to attempt to leave the country while on temporary release, or conduct interviews with local or worldwide media, it added.
When Nick asked him about Foreign Secretary Jeremy Hunt's role in the release, Mr Ratcliffe replied: "He's been very emotionally supportive".
"I didn't tell Gabriella or for a long time my mum - so if it didn't happen I would be the only one to suffer".
Hunt's predecessor Boris Johnson attracted criticism for appearing to jeopardise Zaghari-Ratcliffe's case previous year when he suggested at a parliamentary hearing in November 2017 she had been training journalists in Iran prior to her arrest.
In May, Zaghari-Ratcliffe was summoned to court without a lawyer present under a new charge of "spreading propaganda" against the government.