"I welcome this new sign of confidence by the major airline companies taking part in this unprecedented commercial deal," Airbus's chief operating officer, Fabrice Bregier, told AFP at the Dubai Air Show.
"It's an overwhelming success for Airbus and its A320 aircraft," he said.
The order is for 273 A320neos and 157 A321neos, the revamped and more fuel efficient version of Airbus's most popular single aisle passenger jet, the A320.
The final amount of the contract was not revealed, since it is customary for aircraft manufacturers to grant rebates on the list price, depending on the volume of the order.
The contract will more than double Airbus's current order book for this year, which had stood at 288 planes at the end of October.
It will also place Airbus, with a total 718 orders this year, ahead of its arch-rival Boeing which has 605 orders.
It will bring the total number of orders for the A320 to more than 13,700 since the aircraft went into service in 1988, making it one of the best-selling planes in aviation history.
Airbus's total order book should now increase to more than 7,000, giving it enough work for around nine years at the current rate of production.
Indigo Partners is a US investment firm founded by Bill Franke that specialises in the lease of planes to low-cost airlines.
The A320neo and A321neo jets feature new generation engines that use 15 percent less fuel compared to their peers.
The total number of orders for A320neos since the aircraft was launched in 2010 now stands at more than 5,500.
By comparison, rival Boeing has received more than 4,000 orders for the different versions of its equivalent aircraft, the 737 MAX.
The deal marks a major coup for Airbus's Chief Operating Officer John Leahy, who is expected to leave the group soon at the end of a career in which he oversaw the sale of nearly 15,000 planes.
So far at the Dubai Air Show, Airbus has been very much overshadowed by Boeing.
The European plane maker had been hoping to announce the signing of another major contract for more than 30 of its flagship long-haul jet, the A380, to Emirates Airlines.
But the deal has not been announced so far and negotiations are still ongoing, even if it could nevertheless still be announced in the coming weeks or months.
By contrast, on Sunday, Emirates Airlines agreed to purchase 40 Boeing 787-10 Dreamliners for $15.1 billion at list price, its chief Sheikh Ahmed bin Saeed al-Maktoum said.
Emirates is already the world's largest client for Boeing's 777, with 165 jets and another 164 on firm order.
On Tuesday, Airbus said it had signed a memorandum of understanding with Kuwait's Wataniya Airways for an order of 25 A320neo at a catalogue price of $2.7 billion.
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