Six return flights per week will operate between London Heathrow and Tehran, which BA described as "an important destination".
It follows the lifting of some sanctions against Iran in January and the reopening of the British embassy in the Iranian capital in 2015.
BMI was the last UK airline to fly to Iran, but the service ended in 2012.
The BA Boeing 777 is due to depart from Heathrow just after 21:00 BST.
BA offered the first scheduled flights between London and Tehran in 1946.
However, it ended its service - which at the time was provided by franchisee British Mediterranean Airways - in 2007.
The flights were then operated by British Midland International (BMI), but services were suspended in 2012 as part of BMI's integration into British Airways.
The British embassy in Iran reopened in August last year, after it was ransacked by a mob in 2011.
The reinstatement of regular UK flights also comes 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.
BBC diplomatic correspondent James Landale said BA's decision to resume direct flights may help to improve the UK's relationship with Iran.
Air France resumed flying to Tehran in April after a seven-year break.