It will be the first direct flight by a UK carrier to Iran since 2012, when the route became commercially unviable because relations had broken down.
It follows the lifting of some sanctions against Iran in January and the re-opening of the British embassy in the Iranian capital in 2015.
BA said it will run flights six days a week from London Heathrow.
The Boeing 777 will depart just after 21:00 BST on Thursday.
BA, which offered the first scheduled flights between London and Tehran in 1946, ended its three-times-a-week service in October 2012, a year after the British embassy was closed in the Iranian capital.
The embassy had been stormed by protesters during a demonstration against sanctions over its nuclear programme.
But after a long-term deal on Iran's nuclear programme was agreed with six world powers - the US, UK, France, Russia, China and Germany - in 2015, the British embassy in Tehran reopened.
BBC diplomatic correspondent James Landale said BA's decision to resume direct flights may help improve the UK's relationship with Iran.
Air France resumed flying to Tehran in April after a seven-year break.