Ardian is an independent private investment company and AENA is a leading airport operator.
The €518 million sale was first announced by former owner, abertis, on August 1.
The new owners were attracted by strong growth at the airport, which has seen passengers rise from 3.4 million in 1998 to 10 million currently.
The numbers should be further boosted by plans submitted to the Luton Borough Council to expand and improve the airport.
Luton Airport’s MD, Glyn Jones, said: “Our new owners arrive at an exciting period of change that will see the airport transformed.
“They come with a detailed knowledge of investment in transport services and infrastructure plus an impressive track record in airport operations.”