Prime Minister Andy Burnham said tens of thousands of jobs will be supported with the money
The nuclear-armed submarines are set to replace the current Vanguard Class when they enter service and will be capable of launching Trident 2 D5 ballistic missiles.
They will be powered by a Rolls-Royce nuclear propulsion system, produced in Derby, giving them almost unlimited range.
HMS Dreadnought is the first of four new nuclear submarines.
While the money will support the first boat’s progress towards being ready for service, some of the cash will go towards getting the second boat, HMS Valiant, to its sea trials phase.
Manufacturers will also be supported to get the third and fourth boats through their construction phases.

The Prime Minister’s announcement on Thursday will follow his pledge to tackle joblessness among young people.
On a visit earlier this week to Alstom, a rail manufacturer in Derby, Burnham, RIGHT, said the “first thing” he needed to do was stop the rise in young people not in education, employment or training (Neet).
“To every young person across the country, I want you to know that there is a path for you into a reindustrialised Britain and it starts with the apprenticeships we are funding through this investment today.”
The latest data, published in May, showed the number of young people aged 16-24 neither working nor learning passed one million for the first time since 2013, reaching 1.01 million in the three months from January to March.
“It would be wrong to blame the young people when we have an education system that doesn’t set them up properly, where some struggle to find opportunities at 16, where work experience and work placements aren’t there for them,” Burnham said.