Lauda's bid was preferred over Anglo-Spanish group IAG/Vueling. It was the third offer the former Formula One driver had made since September for Niki -- formerly a unit of now bankrupt Air Berlin, and most recently operated by
"At the end of a transparent tender, (the company) Laudamotion GmbH came out early in the morning as the best bidder," Niki's Austrian and German administrators said in a brief joint statement.
No details of the transaction have been revealed so far.
Lauda sold the airline to Air Berlin in 2011.
The administrators had specified the need for a swift green light from the authorities of the two countries for finalisation of the deal.
IAG announced late last month it had been selected, as part of Air Berlin's liquidation procedure, to purchase "up to 15 A320 aircraft and a portfolio of attractive slots" owned by Niki.
The cost of the transaction, which was to be finalised at the end of February, was set at 20 million euros ($24.5 million), plus up to 16.5 million euros to provide liquidity for the company.
British Airways owner IAG had indicated plans to hire about 740 of Niki's 1,000 employees.
However the bidding procedure was relaunched in mid-January after Austria said it fell under its remit as Niki's head office was in that country.
Besides IAG/Vueling and Lauda, Irish budget airline Ryanair had also wanted to compete for the tender offer in four months.
Niki, whose fleet of around 20 planes served resorts in southern Europe and north Africa, opened insolvency proceedings on December 13th.
The move came after German giant Lufthansa, which had wanted to buy the holiday airline together with large parts of Air Berlin, had to abandon its plans because of EU competition concerns.
Niki ceased flying the next day, stranding thousands of passengers.
The 68-year-old three-time Formula One champion had run a very active campaign to win the bid, promising that the company would be preserved in its entirety.
"From March 2018, Niki will live again as Austrian carrier with headquarters and operational platform in Vienna," he had assured last week in an open letter.
"If my offer is successful, we will give back together the momentum to the company and to Austrian and European air transport."
He also promised "job offers" for all employees of the company, whose aircraft have been grounded since December.
The government in Vienna has looked favourably on the return of the company to Austrian control while the country's air transport industry is largely dominated by Lufthansa.