The allegations were first made in a BBC Panorama programme in 2015.
BAT said that it had been investigating the claims through external legal advisers and it had been co-operating with the SFO.
The firm said it also intended to co-operate with this formal investigation.
Paul Hopkins, who worked for BAT, a British company, in Kenya for 13 years, told Panorama he had begun paying bribes after being told it was the cost of doing business in Africa.
The payments were aimed at influencing laws surrounding the use of tobacco in the region.
The SFO confirmed it was “investigating suspicions of corruption in the conduct of business by BAT plc, its subsidiaries and associated persons”.
It asked those with “information relevant to this investigation, please contact the SFO through its secure and confidential reporting channel”.
The Panorama programme alleged that BAT, whose brands include Dunhill and Pall Mall cigarettes, had made illegal payments to politicians and civil servants in East Africa.
The BBC spent five months investigating and was shown hundreds of secret documents purporting to show backhanders to various officials, including MPs and even people working for a rival company in East Africa.
BAT told Panorama at the time: “The truth is that we do not and will not tolerate corruption, no matter where it takes place.”
Following the news of the official SFO investigation, BAT said in a statement: “As previously announced, we are investigating, through external legal advisers, allegations of misconduct.
“We have been co-operating with the Serious Fraud Office (“SFO”) and British American Tobacco (“BAT”) has been informed that the SFO has now opened a formal investigation. BAT intends to co-operate with that investigation.”
The SFO, which Prime Minister Theresa May suggested during this year’s election campaign should be closed down, has this year fined engine maker Rolls-Royce £500m for bribery and Tesco £130m for mis-stating its accounts.
Shares in BAT were down almost 4% at the start of trading before recovering to a gain of 2%.
They have had a rocky ride in recent days after the US Food and Drug Administration announced it planned to reduce nicotine levels in cigarettes. Its shares have lost about 10% since the FDA’s statement on Friday.
Source: BBC News