"The Commission concluded that the transaction would raise no competition concerns in the European Economic Area," it said in a statement.
LaudaMotion is the company through which former motor racing champion Niki Lauda re-acquired in January 2018 the assets of NIKI, the leisure air carrier he founded in 2003 and which was later integrated into Air Berlin.
Ryanair agreed in March to buy a majority stake in the new Austrian leisure airline in a major push on the German and Austrian markets dominated by Lufthansa.
The Irish airline, Europe's largest low-cost carrier, had agreed to buy an initial 24.9 percent stake in Vienna-based LaudaMotion. That would rise to 75 percent "as soon as possible", subject to EU regulatory approval, the airlines said.
(Reporting by Alastair Macdonald, Philip Blenkinsop, editing by Alexandra Hudson)