As part of the deal the engineering firm will invest in its Derby manufacturing plant, creating 300 jobs.
"This demonstrates the high level of trust the Ministry of Defence has in both our technology and the expertise of our highly skilled workforce," said Jason Smith, Rolls-Royce's chief operating officer and submarines unit president.
Prime Minister David Cameron has stated that his goal is to establish a new fleet of submarines to ensure Britain's independent nuclear capability survives beyond 2028.
Defence Secretary Philip Hammond, speaking yesterday on BBC’s Sunday Politics said that the government is committed to keep a “credible nuclear deterrent”.
However, the final decision as to whether Trident will be replaced is not due to take place before 2016.