It had refused to give them up for days, despite admitting that panicked Revolutionary Guards shot down the Ukrainian passenger jet 752, killing all 176 on board, including three Britons.
Fifty seven were Canadian, and Prime Minister Justin Trudeau said the flight recorders should be sent to France, one of the few countries able to read them.
Hassan Rezaifar, in charge of accident investigations at Iran’s Civil Aviation Organisation, said the black boxes would be sent to Kiev initially, adding: “If this effort is unsuccessful then the black box will be sent to France.”
Russian Foreign Minister Sergei Lavrov said Iran had been “on edge” when the jet was downed on January 8, due to tensions unleashed by the US assassination by drone strike of Iran general Qassem Soleimani.
Iran’s supreme leader Ayatollah Ali Khameini encouraged worshippers on Friday to chant “Death to America”.
He also criticised Britain, France and Germany for invoking a dispute mechanism over Iran’s violations of a nuclear deal, which could lead UN sanctions being reimposed.
The ageing cleric dismissed pro-Western protests rocking the country and said: “These American clowns who lie and say they are with the Iranian people should see who the Iranian people are.”
US President Trump replied: “Their economy is crashing, and their people are suffering. He should be very careful with his words.”
Protests which began across Iran in November were reignited last week when the regime admitted downing the plane.
Iranian dissident Reza Amiri, who recently escaped Tehran’s notorious Evin prison – where British charity worker Nazanin Ratcliffe is held – also spoke out.
The 32-year-old said: “People in the West blame Donald Trump and his sanctions for pushing the regime too far. But this regime has been at war with its own people for 40 years.”
Security forces have been ordered to use whatever measures necessary to quell dissent, and more than 1,500 citizens, including 400 women and children, have been killed by police.
More than 12,000 people have been arrested for taking part.
On Wednesday Reza Pahlavi, once in line to succeed his father the Shah to the Peacock Throne, said the regime was just “months” from collapse.
“This is not dissimilar to the last three months in 1978 before the revolution,” he said.
“I think people smell the opportunity for the first time in 40 years.
“The people have had enough.”