The contract for 12 Typhoon and eight Hawk aircraft was welcomed by Prime Minister David Cameron, who will visit the Middle Eastern state later.
BAE said it is an important export contract and supports its strategy to grow international markets and export business.
The aircraft will be built in the UK and will help to sustain 6,000 high technology and engineering jobs across sites in Warton, Lancashire; Samlesbury, Lancashire; and Brough, East Yorkshire. Aircraft manufacture will begin in 2014 with delivery expected in 2017.
The Omani ministry of defence becomes the seventh operator of Eurofighter Typhoon and the third export customer, after Saudi Arabia and Austria. BAE said there is great interest in the Typhoon and Hawk aircraft.
Guy Griffiths, group managing director for BAE Systems' International business, said: "Receiving this contract is an honour and is excellent news for both BAE Systems and the Eurofighter Typhoon consortium. 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. 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."
Before his arrival in Muscat, the Prime Minister dismissed concerns about Britain selling arms in the region, saying: "Boosting exports is vital for economic growth and that's why I'm doing all I can to promote British business in the fastest-growing markets so they can thrive in the global race."
Business Secretary Vince Cable said: "This is obviously a very good day for BAE Systems, its suppliers and the broader Eurofighter supply chain. The Typhoon programme supports an estimated 8,600 jobs across BAE Systems, Rolls-Royce and Selex-Galileo and their supply chains, with an estimated further 1,500 jobs dependent on export opportunities.
Conservative MP Mark Menzies, whose Fylde constituency includes the Warton site of BAE Systems, said: "This is fantastic news for the employees at Warton and for the economy of Fylde as a whole. I am extremely pleased the hard work by BAE Systems and this Government has secured this deal and, in doing so, has safeguarded the future of many jobs at the site."