It will fund the building of reactors which power a new submarine fleet.
The move, which will create 300 new jobs is likely to stoke tensions between the Tories, and the Liberal Democrats which are opposed to the move.
As part of the deal, Defence Secretary Phillip Hammond will announce the refurbishment of the Rolls-Royce plant at Raynesway in Derby, which has built the nuclear reactor cores for Royal Navy submarines since the 1960s.
The Ministry of Defence has already set aside £3bn to begin work on the new submarines to replace the Royal Navy’s four Vanguard class boats.
The additional money will go towards refurbishing the Rolls-Royce facility and developing the reactors.
It will fund two reactors, one for the seventh Astute Class attack submarine and one for the first of the new nuclear deterrent submarines.
Last month, the government announced it had given £350m of new contracts to design the new submarines to BAE Systems, Babcock and Rolls-Royce.
It is understood that Lib Dems are opposed to the cost and the scale of a replacement Trident programme, which was introduced at the heigh of the Cold War. The UK Trident programme was announced in July 1980, and patrols began in December 1994.
Since 1998, Trident has been the only British nuclear weapon system in service.
Its stated purpose is to provide “the minimum effective nuclear deterrent as the ultimate means to deter the most extreme threat.”