She said she was “overwhelmed” and it would be “awesome” for her four-year-old daughter to “have a mummy again”.
Foreign Secretary Jeremy Hunt said her imprisonment was a “gross injustice” and the release should be permanent.
The Free Nazanin campaign group said a three-day release was “standard practice” ahead of lengthier times out of jail and her lawyer was due to apply for an extension on Saturday.
Her husband Richard Ratcliffe said her temporary release was a “happy surprise” and she is with family in Damavand.
Mrs Zaghari-Ratcliffe, who works for the charity Thomson Reuters Foundation, was arrested at Tehran airport after visiting her family on holiday.
Iranian authorities have accused her of espionage but she insists the visit was to introduce her daughter to her family.
In a statement issued by the Free Nazanin campaign, Mr Ratcliffe said his wife was still in her nightclothes when she was given 10 minutes notice on Thursday morning that she was being released until Sunday 26 August.
The campaign group said the possibility of release had been discussed for several weeks but there had been “a number of false dawns”.
She was released on condition she does not:
Conduct interviews with the media
Visit a foreign embassy, especially the UK’s
Attempt to leave Iran
Free Nazanin said Mrs Zaghari-Ratcliffe and her father have both separately promised she will obey the rules.
She said: “It will be just awesome for Gabriella to have mummy home finally. We can play with her dolls house and she can show me her toys.
“The thought of brushing her hair, and giving her a bath; of being able to take her to the park, and feed her, and sleep next to her – it just kills me. It is still so hard to believe.
Mr Ratcliffe has campaigned for her release since she was jailed and met Foreign Secretary Jeremy Hunt earlier this month, who vowed to do “everything we can to bring her home”.
The campaign thanked “all those involved in making this possible in Tehran and London, and the new foreign secretary”.
Mr Ratcliffe said: “Furlough is not full freedom – we want her home, not just on holiday from prison – but after 873 days it is a massive step.”
Mr Hunt called the release “really good news” with credit going to the “tireless campaigning” of Mr Ratcliffe and the family’s friends.
He also thanked the Iranian authorities “whilst not forgetting that she should not be in prison in the first place”.
“Nazanin is innocent,” the foreign secretary added.