Announcing the deal along with Boeing at the final trade day of the Singapore Airshow, Air Niugini chairman Sir Frederick Reiher said the carrier needed the planes "urgently".
The airline currently has a domestic service, as well as flights to Australia, Singapore, Fiji, the Philippines, Solomon Islands, Hong Kong, Vanuatu and Japan. It is planning to fly to China in the near future.
Dinesh Keskar, regional senior vice president for sales at Boeing Commercial Airplanes, said the aircraft had its first test flight in late January and was "performing exceptionally well".
Boeing's 737 aircraft family competes with European rival Airbus' A320 series in the single-aisle market where the planes are favoured for short to medium-haul routes because of their fuel efficiency.
The Singapore show, considered the biggest in Asia and held every two years, has seen markedly fewer orders for aircraft this time around amid a global economic slowdown led by China that has impacted travel demand.
On Wednesday, Airbus said it had won an $1.85 billion deal for the purchase of six A350-900s by Philippine Airlines (PAL), the flag carrier of one of Asia's fastest-growing economies.
Boeing also announced a commitment from China's Okay Airways to buy 12 aircraft for $1.3 billion despite a weakening Chinese economy.
The biggest deal announced at the show was from Vietnamese budget carrier VietJet Air, which said Thursday it had signed a $3.04 billion contract with US engine maker Pratt & Whitney.
The engines will power the 63 Airbus A320neo and A321neo aircraft ordered by the carrier.