A pounds 7m contract is due to be signed this week between the Greek transport ministry and BA's consultancy arm, Speedwing, to run the airline until the end of 2001.
A former BA executive, Rod Lynch, who resigned last week as chief executive of BBC Resources, will be brought in as managing director of Olympic Airways.
BA will be entitled to buy up to 20 per cent in the airline once it is sold off, provided its finances have been turned around.
Olympic Airways received pounds 1bn from the Greek government five years ago tied to a restructuring programme. Despite this it still lost pounds 15m in 1997.
The airline employs 9,000 staff, has a fleet of 35 aircraft and flys to 75 domestic and international destinations. Next year it will move operations to the new Athens airport.
Among the issues Speedwing will advise the airline and the Greek government on is the choice of an international alliance partner. BA sources denied that it would automatically be lined up to become a member of BA's Oneworld alliance.
In winning the management contract, BA beat off competition from American Airlines, one of the members of Oneworld, United Airlines and Lufthansa.
News of the deal comes as Air France prepares to announce today that it is forming a major transatlantic alliance with Delta Airlines of the US. Lufthansa is already teamed with United, and KLM with Continental and Northwest.