The European aircraft maker Airbus announced the order at the Farnborough International Air Show late on Wednesday.
John Leahy, chief salesman at Airbus, said: "AirAsia's order for 40 Airbus A320 jets is worth $2.7 billion at catalogue prices, although airlines normally negotiate discounts on orders."
The order is added to 60 A320s that AirAsia ordered last year for nearly $4 billion.
"The huge order is all part of fleet expansion to support growth in domestic and regional markets," a spokesman for the airline said.
Competition between national carrier Malaysia Airlines and AirAsia has been strong over the last year as Malaysia airlines announced losses in 2005.
Tony Fernandes, chief executive of AirAsia, said: "The additional purchase was critical to AirAsia's expansion in Malaysia following a route revamp from August that will see it take over the bulk of domestic services from rival Malaysia Airlines.
"With the [domestic route] rationalisation clarified, we are now aware of our growth plans and we need more aircraft."
AirAsia plans to replace the group's Boeing 737-300 fleet with the new jets, which will give it greater operational efficiency, according to Fernandes.
"The A320 has heralded a new era for AirAsia. The sophistication of these aircraft has enhanced our image and brand and enabled us to capture a wider market segment than previously," he said.
AirAsia is the region's only publicly listed budget carrier and now has about 40 planes in its fleet, including seven new A320 jets from its earlier purchase of 60 planes.
The possibilty of new routes to China and India were announced this week.