Aras Amiri, 34, was arrested and detained on bogus spying charges, while visiting her elderly grandmother in Tehran in March 2018.
She has been acquitted by the Supreme Court in Iran of all charges, following a successful appeal lodged by her lawyer, the cultural organisation said in a statement.
Ms Amiri, an art student, was collaborating with the British Council, establishing cultural ties between Iran and the UK.
It was alleged that she had used contacts with arts and theatre groups to "influence and infiltrate" Iran at a cultural level, and that she had confessed to cooperating with British intelligence.
Her fiance James Tyson had accused the Iranian government of using Ms Amiri as a “bargaining chip.”
Retired engineer Anoosheh Ashoori, from Lewisham, has been detained in Evin Prison, Tehran, since August 2017.
He was arrested by Ministry of Intelligence agents for alleged links to Israel during a three-week visit to see his elderly mother, and sentenced to 10 years in prison, despite never having visited Israel or knowing any Israelis.
His wife Sherry Izadi is delighted with the news of Ms Amiri’s release, but said she doesn’t think the British government played much of a role in it.
“We’re delighted for Aras’ family, we know how hard they tried to bring about her release,” Mrs Izadi told LondonWorld.
“We’re really delighted she can take up her life again after such a long interruption.
“Honestly I don’t think the British government has played much of a role in this.
“I think it’s solely due to the efforts of her family and I think it’s Iran in a way sending signals saying: ‘If we want to release someone we can do so at our own leisure.’
“The Supreme Court overturned her guilty verdict exactly at the time when we did our protest outside Number 10 on the anniversary of Anoosheh’s detention on August 13.
“I don’t think it’s coincidental that this happened at that time, there are quite a few political messages behind this release.
Ms Amiri’s return to the UK comes as Iran is negotiating with world powers in Vienna in an effort to revive a 2015 nuclear deal.
Tehran recently said it had also been discussing with the UK its £400m debt for an abandoned tank deal.
Nazanin Zaghari-Ratcliffe’s husband Richard told the BBC that he hopes that Ms Amiri’s release is a good sign to rest of the relatives with families currently detained in Iran.
"We hope it is a good sign for the rest of us.
“Though across all the British cases the signals are mixed, with some potential new releases alongside some potential new cases."
He added: "We are watching closely what happens in the negotiations in Vienna, to see what that means downstream for us."
The British Council said: “We have always refuted the original charges made against Aras.
“We are very proud of her work in our London office as an arts programme officer supporting a greater understanding and appreciation of Iranian culture in the UK.
“This was important work which reflects the value of cross-border cultural collaboration.”