Ghavami, a law graduate from West London, was arrested in June after attempting to watch a men's volleyball match at a stadium in Tehran. She had been with a group protesting against the country's ban on women attending sporting events.
She was later charged with spreading propaganda against the state and has so far served five months of her year-long sentence.
Ghavami is said to be at home with her parents in Tehran pending a decision from the court of appeal. She has been banned from leaving the country for two years.
Her family was concerned about her health following two consecutive hunger strikes in prison. "She just needs to recover now," her brother said.
A worldwide campaign had been launched in an attempt to secure her release. Amnesty International described her as a prisoner of conscience who was being punished by Iranian authorities for demanding equality.
The news of her release was welcomed by her local MP Andy Slaughter, who thanked the public for joining the campaign to free her. "Support for her has come from around the world. Ghoncheh is a young woman of great courage," he said.
But he stressed that more needed to be done to ensure that all the charges against her are dropped and she is free to travel outside of Iran. He also said he would be meeting with Foreign Office ministers later this week to discuss what more the British government could do to ensure her freedom.
British woman jailed for trying to watch volleyball in Iran
3 November
A British-Iranian activist has been found guilty of spreading anti-regime propaganda and sentenced to one year in prison in Iran.
Ghoncheh Ghavami, 25, was arrested in June with several other women who were trying to attend a volleyball match in the capital Tehran. The group had been protesting against the country's ban on women attending sporting events.
"We're stunned, still trying to take it in," her brother, Iman told The Times. "But the family is still fighting, trying to get her out."
He said his sister was not even aware of her sentence yet, as it was not delivered in open court and she has not had any contact with her lawyer or family.
She was a student at the School of Oriental and African Studies (SOAS) in London but was in Iran working with a children's charity and visiting family.
Her sentence has been widely condemned by human rights organisations. Amnesty International says she has been repeatedly denied access to her lawyer or family. Ghavami has also suffered both physical and psychological abuse, with her family reporting that she has been told she "would not walk out of prison alive."
Her family believes she was singled out for being a British national and accused of planning the protest to "embarrass" the Islamic republic.
She has so far spent five months in jail and 41 days in isolation in Section 2a – a maximum-security wing for political dissidents in the country's notorious Evin prison. She is said to still be recovering from a hunger strike which ended three weeks ago.
"Section 2A is one of the most horrible places in the country," her brother said. "The first priority is to get her out of there, into the general prison, where she can interact with other prisoners."
The Foreign Office has said it is investigating her case.
"We have concerns about the grounds for this prosecution, due process during the trial, and Miss Ghavami's treatment whilst in custody," it said in a statement. David Cameron has reportedly discussed the matter with authorities, but said the UK had limited diplomatic powers in Iran.
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