The order includes 100 Airbus A320neo and 100 Boeing 737Max8, both of which are designed to be fuel efficient, and the right to buy a further 150 planes.
The airline said the deal was the largest in European aviation history.
Delivery of the planes is due to begin in 2016.
"Today is a historic day for Norwegian," said the airline's chief executive Bjorn Kjos.
"We have secured our fleet renewal for years to come and are very pleased with the agreements with both Airbus and Boeing."
Norwegian operates 261 routes to 100 destinations and has approximately 2,500 employees.
The company says it is the second largest airline in Scandinavia and the third largest of its type in Europe.
Low cost airline Norwegian Air Shuttle has said it has signed a deal to buy 222 new planes from Airbus and Boeing for a total cost of 127bn Norwegian krone ($21.5; Â£13.9bn).