Indigo, whose interests include Europe’s Wizz Air, US-based Frontier, and Mexico’s Volaris, will buy Airbus’s A320neo family of aircraft.
The order on the penultimate day of the Dubai Airshow comes after what could have been a difficult week for Airbus.
On Sunday, Emirates appeared to snub Airbus over an A380 superjumbo deal.
Indigo’s managing partner, Bill Franke, 80, flew to Dubai for the signing ceremony, although there are still final details of the deal to be worked out.
He said these should be completed by the end of the year.
‘Fits the bill’
The Airbus aircraft, whose wings are made in the UK, will be deployed across Indigo’s airlines, which also includes JetSmart in Chile.
They operate what Mr Franke called an “ultra-low cost model… To be successful you have to have a plane that can be worked hard. Airbus fits the bill.”
The Indigo deal more than doubles Airbus’s existing order book for the year, which stood at about 290 aircraft as of the end of October.
Wednesday’s deal beats a 2015 order for 250 single-aisle planes valued at $27bn by Indian budget carrier IndiGo. The two companies are unrelated.
Despite the headline list price of the Indigo order, airlines typically get discounts on bulk-buys. “Regretfully, Indigo will not be paying $49.5bn,” said Airbus sale chief John Leahy when asked about discounts.
Clinching the deal was seen as a personal triumph for Mr Leahy, who retires at the end of the year after 20 years at Airbus and who had said he hoped to clinch one more big order before going.
He has sold more than 15,000 jets worth an estimated $1.7 trillion.
The Airbus announcement beats an order unveiled earlier this week by arch rival Boeing, which secured a $40bn deal for 787 Dreamliners from Emirates.
That announcement, on Sunday, was due to be unveiled alongside an Emirates’ order for A380s.
But the A380 announcement was cancelled minutes before a press conference convened. It is thought that Emirates asked for last-minutes changes.
Mr Leahy declined to say if the A380 deal could this happen this week. “You’ll just have to walk over there [to Emirates’ show chalet] and ask them,” he told reporters.
Meanwhile, Boeing on Wednesday announced an order from Gulf airline flydubai for 225 medium-haul 737 MAX aircraft with a list price of $27bn, hailing it as the “largest-ever single-aisle jet order” from a Middle East carrier.
Analysis by Dominic O’Connell, Today business presenter
Airbus’s celebration of Indigo’s massive order for the A320 NEO – which at $49.5bn is its biggest ever single deal – will be muted.
The Dubai show has shown up the sharply contrasting fortunes at each end of the European plane maker’s product range.
Its smallest plane, the A320, is selling like hot cakes. It can’t make them fast enough.
The largest plane, the superjumbo A380, can’t find a buyer. Airbus can’t make them slowly enough.