This follows previous contracts awarded to BAE Systems in 2012 valued at £328m and £315m to commence initial design.
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."
Around 6,500 people are employed at BAE Systems' site in Barrow, where the Company is also building the Astute class - seven nuclear-powered attack submarines for the Royal Navy.