Several different models from the Falcon III series will be provided and form part of a broader tactical communications system, a statement from Harris said.
The radios provide high-performance, line-of-sight and beyond-line-of-sight voice and data communications, including wideband networking.
The order, which includes logistical and field support, was received in the third quarter of Harris's 2013 fiscal year, the statement said.
"Harris radio systems will establish a secure communications backbone for the Royal Brunei Armed Forces and its modernization program," Brendan O'Connell, president of international business at Harris RF Communications, said.
"These tactical systems will enhance situational awareness and speed decision-making."
Brunei, with a population of just more than 400,000, is on the north coast of the island of Borneo and has a coastline on the South China Sea.
The sultanate occupies around 1 percent of the island and is surrounded by the Malaysian state of Sarawak. It also is separated into two parts by the Sarawak district of Limbang.
Indonesia occupies almost 75 percent of Borneo, to the south of the Malaysian state.
Other recent Asian orders for Harris's Falcon III radios include a $29 million deal from an undisclosed country for its wideband manpack version, announced in early April.
"The nation is acquiring the company's new RF-7800H high-frequency wideband manpack and RF-7800W high-capacity line-of-sight radios," a statement from Harris RF Communications said.
Harris said the RF-7800H is the world's first HF radio with high-speed wideband data capabilities that allows users to efficiently transmit large data files such as images over very long range beyond-line-of-sight links.
The RF-7800H also is 20 percent smaller and lighter, Harris said.
Harris also received a $23 million order from Australia for software upgrades, the company's fiscal 2013 third quarter results statement said.
Harris Corp., which has headquarters Melbourne, Fla., also reported group revenue in the third quarter of fiscal 2013 of $1.2 billion compared with $1.37 billion for the same period 2012.
Revenue in the third quarter for Harris RF Communications division, which makes the Falcon III, was $418 million compared with $538 million in the previous year. Sales of tactical communications were $276 million, a 31 percent drop, and sales of public safety radio equipment totaled $142 million, increasing 2 percent.
Harris operates in more than 125 countries employing about 15,000 people and has annual revenue of around $5.5 billion.