The service was suspended in October 2012. Six return flights per week will operate between London Heathrow and Tehran, before a daily service will start later this year.
BA described the Iranian capital as “an important destination” for the airline, according to the Guardian.
The resumption of flights on Thursday follows the lifting of sanctions against Iran in January.
The then British foreign secretary Philip Hammond said at the time that British firms should take advantage of the opportunities that would open up.
The first BA plane to Iran, a Boeing 777, will depart from Heathrow at 9.10pm. Flights were initially due to resume in July but there was a delay in establishing the route.
A BA spokeswoman said: “The Iranians have been extremely helpful in setting up this important new route and have been as keen as we are for the service to start.
“Tehran is an important destination for British Airways and we wanted to ensure that the service we offered met the highest standards our customers rightly expect of us from day one.”
Air France resumed Paris-Tehran flights in April after an eight-year break.
International interest in ties with Iran has been growing since Tehran and the Group 5+1 (Russia, China, the US, Britain, France and Germany) on July 14, 2015 finalized a comprehensive nuclear deal and started implementing it on January 16.
The agreement, known as the Joint Comprehensive Plan of Action (JCPOA), terminated all nuclear-related sanctions imposed on Iran.