Sir Michael Bishop, chairman and majority shareholder of British Midland plc, is to sell his stake to Lufthansa.
The deal which is expected to be completed early next year will give the German national carrier a stake of 80% in bmi.
The remaining 20% is held by Scandinavian airline SAS which is also likely to sell it to Lufthansa.
The news of Sir Michael's decision to sell was welcomed by Virgin Atlantic whose ceo Steve Ridgway proposed a tie up between Virgin and bmi.
He said such a tie up would create a "new and even more effective competitor to BA."
The Lufthansa announcement about bmi was buried in an interim report covering January-September 2008 put out today (October 29) by Lufthansa.
The statement said that Sir Michael, who is 66, had on October 10, exercised an option on behalf of BBW Partnership Ltd. which "requires Lufthansa to purchase 50% plus one share in British Midland PLC (bmi)"
The 50% plus one share, Sir Michael's controlling interest in British Midland, is the entire shareholding owned by BBW.
Lufthansa said Sir Michael's option to sell was based on an agreement signed in November 1999.
The German airline added: "The completion of the exercise is expected to take place not before January 12 2009.
"It is subject to anti-trust approval and regulatory requirements.
"Discussions regarding the future structure and options are ongoing between Lufthansa, Sir Michael Bishop and bmi."
The sale if approved will give Lufthansa not only control of the UK's second largest carrier but also about 11-12% of the 9,000 weekly slots at Heathrow.
These slots, second only in number that to those owned by BA, will significantly enhance bmi's value.
One analyst recently described the possession of these slots as a "cash cow" for bmi.
When BA bought 51 slots from bmi in March 2007, it paid about £30m.
Since the Open Skies agreement was signed between the US and the EU, opening up Heathrow to all American and EU carriers, the slots have gone up in value.
When Continental Airlines bought four take off and landing slots at the airport in March this year, just before the Open Skies deal came into force, it reportedly paid £105m for them.
Virgin Atlantic, which runs long haul services to cities including New York, Shanghai and Johannesburg, has often been cited as a front runner to buy bmi.
The airline which is 49% owned by Singapore Airlines, has also been in long running battles with the British carrier, the latest being BA's proposed link up with American Airlines.
Mr Ridgway described Sir Michael as an "icon" of aviation who along with Virgin Atlantic, has helped to provide much-needed competition to BA, and choice for consumers. "
He added: "Now we are about to enter the next phase of bmi's future and a turning point in aviation.
"Everyone has speculated that it would make sense for Virgin Atlantic and bmi to combine their long-haul and short-haul networks.
"There is now a major opportunity to do that and create a new and even more effective competitor to BA.
"I am sure that Lufthansa realises the future opportunities and this could be a really good example of the right industry consolidation.
"It would be good for consumers, for UK plc and European aviation's competitiveness."
Visit www.lufthansa.com, www.flybmi.com and www.virgin-atlantic.com.