A spokesman said: "It is with deep regret that the Foreign and Commonwealth Office confirms the death of a British man onboard Air Algerie flight AH 5107.
"We are providing consular support to his family at this tragic time and we ask the media respect the privacy of those grieving."
Earlier, French soldiers secured one of the black boxes from the plane that crashed in northern Mali with the loss of at least 116 lives, French president Francois Hollande said.
Terrorism has not been ruled out as a cause, although officials say the most likely cause is bad weather.
The black box was recovered from the wreckage in the Gossi region near the border with Burkina Faso and is being taken to the northern city of Gao, where a French contingent is based, Mr Hollande told reporters after a crisis meeting with top ministers.
"There are, alas, no survivors," Mr Hollande said. "I share the pain of families living through this terrible ordeal."
Nearly half of the passengers aboard the flight were French, many headed on to Europe after arriving in the Algerian capital Algiers from the Burkina Faso capital Ouagadougou.
Mr Hollande has said France will spare no efforts to uncover the cause of the crash - the third major plane disaster around the world within a week after incidents in Ukraine and Taiwan.
He added: "There are hypotheses, notably weather-related."