A Ministry of Defense statement said the Bell 212 helicopter went down in Ulu Belait near the western coast as it headed for the capital, Bandar Seri Begawan.
The army said 11 of the 12 who died were cadets on a training mission. The other dead is one of the three crewmembers.
The two survivors being treated at RIPAS Hospital are reported to be in stable condition.
All the bodies were recovered and returned to the Surau of Bolkiah Garrison where relatives and military officials prayed.
An investigation into the accident -- the worse aviation accident in Brunei's history -- is under way.
The Ministry of Defense is deeply saddened by this tragic accident and extends its sincere condolences and profound sympathy to the families and loved ones affected by this tragic loss," the ministry statement said.
"While the exact circumstances of this tragic incident remain to be determined, the Ministry of Defense is taking appropriate action to ascertain the facts."
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 completely 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.
Brunei, as does the rest of the Borneo, has oil and gas reserves as well as timber reserves.
In 1888, Brunei became a British protectorate and independence was achieved in 1984. The same family -- has ruled Brunei for more than six centuries.
Militarily, Brunei is believed to operate nine of the transporter Bell 212 Twin Huey, sometimes called the Twin Two-Twelve.
Brunei also took delivery earlier this year of a Bell 214ST, a larger stretched-fuselage medium-lift version of the 212 manufactured by Bell Helicopter Textron.
The aircraft operate as part of Number 1 Squadron on missions including trooplift, casualty evacuation, medical evacuation, fire suppression and search and rescue
The military also operates Bolkow BO 105, made by Messerschmitt-Bölkow-Blohm, and four Blackhawk S-70A helicopters.
In December Brunei announced it had signed a contract with Sikorsky for 12 S-70i Black Hawks, with an option for 10 more. The S-70i helicopters will gradually replace the ageing Bell and the Bolkow BO 105 helicopters.
Sikorsky's Black Hawk was chosen above the Eurocopter's EC 725 Cougar, AgustaWestland AW139 and Bell 412, DefenseWeb reported at the time.