* Purchase price $24 million, plus additional liquidity
* Final chapter in demise of Air Berlin, former Niki owner
* New Vueling unit to employ 740 former Niki employees (Adds details from Niki insolvency administrator)
FRANKFURT, Dec 29 (Reuters) - British Airways' owner IAG said on Friday it would buy Niki, Air Berlin's insolvent Austrian holiday airline, for 20 million euros ($24.01 million) and provide additional liquidity to the company of up to 16.5 million euros.
The sale to IAG, which had been in exclusive talks for the airline, is the final chapter in the demise of Air Berlin, the No. 2 German air carrier that previously owned Niki and filed for insolvency earlier this year.
IAG said Niki would become part of the low-cost carrier Vueling and would be incorporated in Austria, employing 740 of Niki's 1,000 former employees. Assets include 15 A320 aircraft and slots at airports including Vienna, Dusseldorf, Munich, Palma and Zurich.
"Niki was the most financially viable part of Air Berlin, and its focus on leisure travel means it's a great fit with Vueling," said IAG's chief executive, Willie Walsh.
Niki filed for insolvency earlier this month after Germany's Lufthansa backed out of a deal to buy its assets on competition concerns, grounding the fleet and stranding thousands of passengers.
Niki's administrators had been racing to find a buyer for its assets before it loses its takeoff and landing slots, its most attractive asset.
"Niki is getting a financially strong partner with a long-term development concept," said Lucas Floether, Niki's insolvency administrator. The deal should close in February, he said.
The former Formula One champion Niki Lauda founded the airline in 2003. It was fully acquired by Air Berlin at the end of 2011, according to the company's website, but kept the name.
Lauda made a bid to repurchase Niki, along with several others, but eventually lost out to IAG.
Air Berlin, beloved among Germans for its flights to the holiday island Mallorca and for the chocolate hearts it gave out after each flight, filed for administration in August. A government loan kept its planes in the air during negotiations on breaking it up.
Air Berlin agreed to sell a large part of its airline assets to Lufthansa. It also clinched a deal with Britain's easyJet for some operations at Berlin Tegel. ($1 = 0.8329 euros) (Reporting by Tom Sims; Editing by Larry King)