The official announcement will be made today.
One of the reactors is set to be fitted on the seventh Astute class attack submarine, while the other is expected to be used on the first of a new generation of nuclear submarines.
The deal, which will create 300 jobs, has divided the Coalition government: Conservatives support the full renewal of four Vanguard submarines by 2028, while the Liberal Democrats insist the government should look for cheaper alternatives.
While a final decision on Trident renewal will not be made until 2016, the long lead times forced the government to sign the contracts now. Speaking on the BBC, defence secretary Philip Hammond said: “The actual decision to go ahead and build the reactors won’t have to be made until 2016 and what we are doing at the moment is ordering the things that have to be ordered in order to give us that option.”
Mr Hammond said that a review of the Trident programme confirmed the replacement of Vanguard submarines was the best solution, but the Liberal Democrats insisted the government looks for new technologies. A review is being carried out by armed forces minister Nick Harvey.
The first Vanguard-class vessel was due to leave service in 2022, but the government extended the life of the fleet as part of the 2010 Defence and Security Review.