The contract will sustain the jobs of more than 1,400 employees working at BAE Systems on a programme that has already engaged with more than 240 suppliers.
This follows previous contracts awarded to BAE Systems in 2012 valued at £328M and £315M to commence initial design.
Defence Secretary Michael Fallon said: “The UK has been committed to a continuous at-sea deterrent for more than 45 years. This is because it is the responsibility of the British Government to protect its citizens and provide this vital line of defence. It is therefore crucial that we continue to invest in the Successor programme to be ready for a final decision on renewal next year.
“It is thanks to our long-term economic plan that we are able to invest in this latest wave of design funding, which will help to secure the jobs of hundreds of people working across the MOD’s three main industrial partners working on the Successor programme. This underlines how important this work is to the British economy as well as the future security of the UK.”
The contracts fund the next stage of design work for the new class of submarines, designed to carry the UK's independent nuclear deterrent. The programme recently passed a major design review and is now more than halfway through its five-year Assessment Phase.
Tony Johns, the Managing Director at BAE Systems' Submarines, said: "Designing a new, nuclear-powered ballistic missile submarine is one of the most challenging engineering projects in the world today. The Successor programme is the largest and most complex project we have ever faced. This funding will now allow us to mature the design over the next 12 months to enable us to start construction in 2016."
Approximately 6,500 people are employed at BAE Systems' site in Barrow, where the Company is also building the Astute class - seven state-of-the-art nuclear-powered attack submarines for the Royal Navy. Last year, the Company created 900 skilled jobs and recruitment is set to continue throughout 2015.