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.
Sanctions