The deal, which will help sustain thousands of jobs in Britain, is the first major order since BAE Systems failed to merge with European aerospace giant EADS earlier this year, but failed to boost shares in the British company.
"BAE Systems and the government of the Sultanate of Oman have entered into a contract for the supply of Typhoon and Hawk Advanced Jet Trainer aircraft to the Royal Air Force of Oman," the London-listed company said in a statement.
"The contract, valued at approximately £2.5 billion, provides for the delivery of 12 Typhoon and 8 Hawk aircraft starting in 2017.
"BAE Systems is the prime contractor for both the provision of the aircraft and the agreed arrangements for in-service support."
British Prime Minister David Cameron was in Oman on Friday, and met with Sultan Qaboos to discuss "ongoing cooperation between both countries in several fields in light of their good relations and the mutual interests of their friendly people," Oman news agency ONA reported.
Oman has historically close relations with Britain and is the only Arab state in the Gulf that also has warm ties with neighbouring Iran, enabling it to become a key mediator between Tehran and the West.
Oman will become the seventh nation in the world, and the second in the Middle East, to own the Eurofighter Typhoon.
"BAE Systems welcomes the decision by the Sultanate of Oman to purchase 12 Typhoon and eight Hawk Advanced Jet Trainer aircraft," it added.
"This contract is further recognition that both Typhoon and Hawk are leading aircraft in their class, providing the best capabilities available.
"As well as supplying aircraft, BAE Systems will provide in-service support to the Royal Air Force of Oman's operational tasks. Deliveries are expected to commence in 2017."
The Eurofighter project consortium comprises Britain's BAE Systems, Italy's Finmeccanica and the European Aeronautic Defence and Space Company (EADS).
"Receiving this contract is an honour and is excellent news for both BAE Systems and the Eurofighter Typhoon consortium," said Guy Griffiths, group managing director for BAE Systems' international business.
"BAE Systems has a long history of working in Oman and we are delighted this contract will enable us to continue to work together.
"We believe that Oman has now added the most advanced fighter jet and proven training aircraft, available in the world, to its military portfolio."
He added: "We look forward to working in partnership with Oman's Ministry of Defence, and the Royal Air Force of Oman, to ensure this is a highly successful programme that maximises the potential of both Hawk and Typhoon."
The latest order of Hawk jets takes the total number of Hawk aircraft sold, or on order, to 998 after a separate order from Saudi Arabia in May.
Separately, BAE had warned this week that a lucrative deal to sell fighter jets to Saudi Arabia was facing unresolved "issues" five years after an agreement was struck between the two sides.
BAE and Saudi Arabia signed a £4.5-billion ($7.3-billion, 5.5-billion-euro) deal in 2007 to supply 72 Typhoon jets to Riyadh.
The group said Wednesday that ongoing discussions were centred on acceptable pricing terms. BAE added that underlying earnings per share would be hit if an agreement was not reached soon.
Earlier this year, BAE had attempted to merge with EADS but the deal collapsed under the weight of political wrangling and unexpectedly strong opposition from Germany.
In London, BAE shares had plunged by 2.16 percent 340.50 pence in afternoon trading, while the FTSE 100 index on which they are listed was 0.75 percent lower overall.