The increase from Lufthansa's previous 30-percent holding in BMI, formerly known as British Midland, was the result of an option held by BMI chairman Michael Bishop to sell his stake of 50 percent plus one share to the German carrier.
Scandinavian Airlines (SAS) owns the remaining 20 percent of BMI, which holds slots at London's Heathrow airport worth around 770 million pounds ($1.2 billion dollars) and runs lucrative trans-Atlantic flights.
The deal makes Lufthansa the second biggest carrier at Heathrow, the busiest European hub, after British Airways.
Lufthansa said it was obliged to make an offer for the majority of BMI shares, but the German carrier said in a statement that "this option was not expected before January 12."
Lufthansa was understood to be paying around 318 million pounds ($510 million) for the 50 percent stake, according to Britain's Press Assocation.
SAS has not hidden its interest in selling its stake in BMI, while Lufthansa had said in April that it was interested in taking a majority holding.
The German carrier has been mentioned in several other possible European deals and has already bought Swiss and Brussels Airlines.
The Italian government sounded out Lufthansa as a potential partner in Alitalia, and the German airline is also a front runner in bidding for the Austrian carrier AUA.
That privatisation has been postponed until late December, however.
Lufthansa boss Wolfgang Mayrhuber said Wednesday that "we see the current crisis as a constructive situation and we see opportunities for consolidation."
He added that the method of BMI's integration into the Lufthansa structure was "currently under discussion."
Mayrhuber spoke in Frankfurt during a presentation of Lufthansa's third quarter results.
On Tuesday, the airline cut its 2008 operating profit target to 1.1 billion euros ($1.4 billion dollars) owing to "record" fuel costs, weaker demand and the global financial crisis.
Its third quarter net profit plunged by 75 percent to 149 million euros.
Looking ahead, Mayrhuber said that "rigorous cost managment will always be on the agenda," but added that "we do not forsee outright firings."