The Boeing 777, which departed from London's Heathrow airport at 9.10 p.m, arrived in Imam Khomeini airport at 6.15 a.m, Xinhua news agency reported.
BA will operate six return flights per week between London and Tehran.
BA, which first flew into the Iranian capital in 1946, becomes the second European airline to resume flights into the country, after Air France brought an eight-year break to an end in April.
The resumption of BA flights on Thursday follows the lifting of some sanctions against Iran in January after the International Atomic Energy Agency said the Iranian government had met its obligations as part of a nuclear deal with six world powers.
