Iran said Ms Amiri had confessed to co-operating with British intelligence.
She was detained in March 2018 while visiting her elderly grandmother, and was charged two months later with “acting against national security”.
Ms Amiri’s cousin, Mohsen Omrani, told the BBC that she was currently being held in the same section of Tehran’s Evin prison as Nazanin Zaghari-Ratcliffe, a dual British-Iranian national sentenced to five years in prison for spying in 2016.
Ms Zaghari-Ratcliffe’s husband, Richard Ratcliffe, said the two women had become friends and that they were both chess pieces on the same political board.
A spokesman for Iran’s judiciary, Gholamhossein Esmaili, said on Monday that an unnamed Iranian woman who was “in charge of the Iran desk at the British Council” had been convicted of spying.
The woman had used contacts with arts and theatre groups to “influence and infiltrate” Iran at a cultural level, Mr Esmaili alleged. Once arrested, she quickly and clearly confessed, he added.
The British council initially could not confirm that the woman was one of its employees, but on Tuesday Sir Ciarán said in a statement: “It sadly seems likely that our colleague Aras Amiri is the Iranian national who has allegedly been sentenced by Iranian authorities.”
“We are dismayed by this reported sentence and are profoundly concerned for Aras’ safety and wellbeing, which has been our absolute priority throughout her detention since early 2018.”
Sir Ciarán said Ms Amiri had been “employed for five years in London to help greater appreciation of Iranian culture in the UK, for example supporting translations of Iranian books into English”.
“The British Council does not do any work in Iran and Aras did not travel to Iran for work. We will remain in close contact with the Foreign and Commonwealth Office.”
UK Foreign Secretary Jeremy Hunt said he was “very concerned”.
“We are awaiting details but I am proposing to meet relatives of the individual later this week because we’re very, very concerned about what’s happened and then we’ll do everything we can to support the individual,” he told MPs.