BAE said it was awarded the contract by Boeing, the manufacturer of the 737 aircraft.
"The In-Service Support contract award represents a significant milestone in our journey on the Wedgetail project and builds on BAE Systems' experience as Australia's predominant supplier of integrated EW systems," said Kim Scott, BAE's director of Land and Integrated Systems.
Under the order, worth nearly $43 million, BAE will provide maintenance, engineering and support services.
The Wedgetail carries of crew of six to 10 and is equipped with integrated Electronic Support Measures and EW Self-Protection subsystems developed by BAE Systems Australia.
The twin-engine aircraft has a range of about 4,000 miles and a cruise speed of 530 mph.
BAE Systems said the new contract follows an award for support infrastructure for the early warning aircraft and long-lead procurement of spare parts.