Nazanin Zaghari-Ratcliffe, who works for the Thomson Reuters Foundation and was arrested on April 3, called her husband Richard on Tuesday to inform him of her sentence, he said in a statement.
"Nazanin has been sentenced for five years' imprisonment. The charges justifying this sentence remain secret," he said.
Iran's elite Revolutionary Guards earlier accused Zaghari-Ratcliffe of having taken part in the "sedition movement" of widespread protests that followed the 2009 re-election of former hardline president Mahmoud Ahmadinejad.
Iran does not recognise dual citizenship.
Britain earlier said it had raised the case "repeatedly and at the highest levels" and will continue to do so at "every available opportunity".
At a rally outside the Iranian embassy in London in June, Richard Ratcliffe told AFP his wife was arrested as she prepared to return to Britain with the couple's daughter Gabriella after visiting family in Iran.
Gabriella was born in Britain and has a British passport, which was confiscated by the Iranian authorities, leaving her stranded with her grandparents in Iran.
"She has nothing to do with Iran in her work and the foundation doesn't work with Iran anyway, so we have no idea why she has been detained for more than two months, first in isolation and then in a common cell," foundation CEO Monique Villa told AFP in June.
"Now we don't know because she seems to have disappeared from where she was.
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