The agreement is Airbus' single largest order by number of aircraft, a spokesman for the firm said.
The deal is worth a $26.5bn (Â£17bn) at list prices, although airlines typically get a discount.
IndiGo is India's largest domestic airline by market share, and flies one in three of India's air travellers.
The agreement, which was signed on Saturday, confirms an earlier provisional order by IndiGo for the narrow-body planes which was announced in October.
It is the second-largest order by value for Airbus.
IndiGo was founded in 2006 by travel entrepreneur Rahul Bhatia and Rakesh Gangwal, a former chief executive of US Airways.
The firm has placed a series of orders for Airbus jets as it tries to win a bigger share of India's fast growing aviation market.
The A320neo is a more fuel efficient variant of the widely-used A320 aircraft. It competes against Boeing's upgraded 737 Max.
Airbus has finalised a deal with Indian budget airline IndiGo to sell 250 A320neo aircraft.