News of the deal pushed Lufthansa shares up more than 3 percent to their highest level in almost 17 years.
Lufthansa CEO Carsten Spohr said earlier he expected the European Union to approve the transaction by the end of 2017.
While it conducted the negotiations, Air Berlin's planes were kept in the air by a government loan of 150 million euros.
"Today will be a milestone in the history of Lufthansa and Air Berlin", said Spohr in Berlin ahead of the expected official announcement that a formal deal has been agreed between the airlines. So far, there has been no sign of an agreement between Air Berlin and Easyjet for remaining parts of the business, nor has Lufthansa announced how much it will pay under the deal.
EasyJet declined to comment on the progress of talks on Thursday.
As part of the deal Lufthansa will take over Air Berlin's low-priced leisure airline Niki, its LG Walter regional airline as well as 20 additional aircraft - bringing the total to around 80 planes.
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That sum includes investment in new planes, for which the board freed up 1 billion euros of funds last month, the purchase price and the costs of taking on new staff.
Lufthansa shares were up over 2.9%, which was the highest mover on the DAX market index in Germany in Thursday morning trading.
Air Berlin, Germany's second largest carrier, will cease operating flights this month, capping a turbulent summer for European carriers.
Industry analysts in Europe said they raised ratings on shares of Lufthansa from market-perform to outperform, saying they believe a deal to acquire part of Air Berlin would add between €70 and €90 million in operating profits annually to Eurowings the budget unit of Lufthansa over the medium term.
The national airline of Italy Alitalia is also in administration and is seeking investors and Monarch the leisure airline based in Britain collapsed at the beginning of October.