EasyJet said it expects to complete the transaction "in the near future".
Lufthansa has abandoned plans to buy Air Berlin subsidiary Niki after being told by the European Commission that it would not allow the deal, meaning Niki could join the list of Europe's collapsed airlines this year.
Commissioner Margrethe Vestager, in charge of competition policy, said: "Our job is to make sure that airline takeovers do not result in less competition - that would mean higher flight fares and less choice for consumers".
The German government, which stands to lose out on a loan given to Air Berlin, said it expected Niki, founded by former Formula 1 driver Niki Lauda, to file for insolvency protection and be grounded. Indeed, control over slot portfolios at congested airports can result in higher barriers to entry for airlines wanting to operate to and from those airports, which in turn could result in higher fares for passengers.
The Commission therefore concluded that the proposed acquisition would raise no competition concerns in any of the relevant markets.
Tough competition and falling ticket prices have led to the demise of Monarch and Air Berlin while Alitalia has filed for insolvency protection.
Russia Banned from the 2018 Winter Olympics
They would compete under the title "Olympic Athletes from Russia", and they will be prevented from flying the Russian flag. He did not say what form this support would take.
In the wake of the failed Niki pursuit, Lufthansa is offering to relinquish "numerous slots" to gain clearance for the purchase of Air Berlin turboprop operator LGW, officially known as Luftfahrtgesellschaft Walter.
Air Berlin's insolvency administrator received a number of bids for various Air Berlin assets.
Lufthansa, which wants to purchase Air Berlin units Niki and LGW, will have to give up more airport slots and routes to address competition concerns or face a full-scale European Union investigation, a person familiar with the matter told Reuters last week.
The investigation found that easyJet will continue to face heightened competition from the likes of Lufthansa and Ryanair on most of its German routes, with no negative effect for airline passengers.
However, EU antitrust officials were wary of granting Lufthansa too much market power and weren't willing to accept the remedy package the German airline had proposed.
It has previously said it planned to grow the Eurowings' fleet to about 210 aircraft from 160 as a result of the Air Berlin insolvency.