Ratcliffe and his supporters have held multiple protests and vigils in London to ask for her release in the past two years.
Nazanin Zaghari-Ratcliffe, a British-Iranian woman who has been in prison in Tehran for more than two years following a conviction for spying, was freed for three days on Thursday.
In comments issued by the campaign, Mrs Zaghari-Ratcliffe said she "wasn't expecting it at all" and it was "awesome" for her daughter Gabriella to "have mummy home".
"Initially the release is for three days - her lawyer is hopeful this can be extended", her husband Richard Ratcliffe said in a statement.
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He said he spoke to his wife, who was "full of joy", via Skype, moments after she was released.
The Free Nazanin campaign said that after several weeks of bureaucracy over her possible temporary furlough, Zaghari-Ratcliffe was told earlier on Thursday that she had 10 minutes to get ready because she was being released.
It is the first time Mrs Zaghari-Ratcliffe has been allowed out of prison since her arrest, in April 2016, and conviction previous year for plotting to overthrow the Iranian regime - something she has always denied. She was arrested and convicted on espionage charges, which she denies.
Hunt's predecessor Boris Johnson attracted criticism for appearing to jeopardise Zaghari-Ratcliffe's case past year when he suggested at a parliamentary hearing in November 2017 she had been training journalists in Iran prior to her arrest.
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"Really good news that Nazanin has been released on furlough, credit to tireless campaigning by husband Richard and her friends".
He said there was some indication that this would happen, but there had been a number of "false dawns". She is now with her family in Damavand.
"But being in prison AT ALL is gross injustice and she must be PERMANENTLY released for which every effort will continue".
There has been no clear statement from Iranian authorities about why Zaghari-Ratcliffe was released, but some have speculated it could be a conciliatory gesture to mark the Islamic festival of Eid.
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Ratcliffe said that didn't know exactly how it came about, but added that Britain's new foreign secretary, Jeremy Hunt, was their "lucky charm".