The order for 530 planes, with a catalogue-price value of 26.5 billion dollars (24 billion euros), is a record for Airbus.
It was signed on Indian independence day, 15 August, although the company first announced it would be placed in October 2014.
IndiGo, which is India's fastest-growing airline and, with 38.4 per cent of market share, its largest, ordered 100 A320s in 2005 and they have all been delivered.
In 2011 it became the first Indian company to buy the A320neo, bringing its Airbus fleet to 280.
There are now more than 4,000 orders for the A320neo, an Airbus statement said on Monday.
The plane's acronym stands for "new engine option" and a number of innovations mean that it uses 15 per cent less fuel than its predecessors and should use 20 per cent less by 2020, according to the plane-maker.
That means a reduction of CO2 emission of 5,000 tonnes per plane per year, Airbus claims.