"It is very good news. This order, it is the equivalent of six months of production, of course spread out over several years. This is considerable," said its Chief Operating Officer, Fabrice Bregier.
"It is a great present for the start of the year," he added.
Airbus said the deal with Indigo for 180 A320 aircraft was the largest single firm order for large commercial jets in its history, although it has signed contracts that are worth more financially.
The low-cost airline has signed a memorandum of understanding to acquire 150 single-aisle A320neo jets. The neo versions -- "new engine option" -- are equipped with more efficient engines and fuel-saving wing tips.
IndiGo is the first client for this new version of the aircraft, which Airbus only unveiled last month and plans to start delivering in early 2016.
The other 30 planes are to be standard versions of the A320.
The deal is a major shot in the arm for Airbus, which came under intense pressure last year after Australian carrier Qantas grounded its A380 fleet following an engine blow-out.
"Launching a new product and securing an order of this size, it is the validation for a year of reflection," said Breiger.
The value of the deal was not announced, but is expected to come in lower than the Airbus catalogue price of $15.6 billion (12 billion euros).
"That is a guideline price and does not take into account eventual reductions for bulk purchases," a source close to the deal said.
Shares in parent company EADS jumped 4.63 per cent before dropping back as analysts said the Indian airline would probably be able to renegotiate the price.
IndiGo, India's largest budget carrier by market-share, said it was not immediately sure how it would finance the deal, and it had not decided whether it would conduct an initial public offering.
"We have lots of time [to decide on financing options]," its president Aditya Ghosh told Dow Jones Newswires, adding that the company will consider all options.
"Deliveries of the aircraft start only in 2016," Ghosh said.
The airline's co-founders, Rakesh Gangwal and Rahul Bhatia, said the deal would enable them to continue offering low fares due to fuel efficiencies.
"Ordering more A320s was the natural choice to meet India's growing flying needs. The opportunity to reduce costs and to further improve our environmental performance through the A320neo were key to our decision," they said in a statement.
John Leahy, Airbus' Chief Operating Officer for Customers, said the deal gave IndiGo a strong position in the fast growing Indian air travel industry.
"This order positions IndiGo to take full advantage of the predicted growth in Indian air travel and we are delighted that they continue to build their future with Airbus," he said.
Airbus said it has delivered some 4,500 of the A320 aircraft in its various forms to 310 airlines, with another 1,300 on the order books, making it the world's best-selling single-aisle aircraft family.
The A320neo is Airbus' bid to counter rival aircraft such as Canada's Bombardier CSeries and China's C919, as well as heading off Boeing, which has not yet decided on the future of its medium-haul 737.
Airbus will offer airlines a choice of motors on its A320neo.
They will be able to choose between the latest model from CFM International, a joint venture between France's Safran and General Electric in the United States, and a US Pratt & Whitney engine.
IndiGo had not yet decided what engine it wanted for its models and would make an announcement at a later date, Airbus said.