A Saudi defence ministry statement, carried by the official SPA news agency, said: "The agreement was signed for the purchase of 72 Typhoon aircraft."
Sources close to the negotiations had said a deal signed in December was believed to have an option of up to 72 aircraft.
The brief statement, which did not give the value of the deal, said it also included a defence technology transfer.
The purchase is being carried out to replace British-made Tornados and other jets with the Typhoons.
The multinational Eurofighter consortium that makes Typhoon jets includes British defence contractor BAE Systems Plc, European aerospace group EADS and Italy's Finmeccanica.
BAE is expected to invest in local training for thousands of Saudi nationals.
Saudi Arabia has a history of buying arms from Britain dating back to the 1960s, and usually pays in oil.