The Astute submarine has the latest stealth technology, a world-beating sonar system and is armed with 38 torpedoes and missiles - more than any previous Royal Navy submarine.
The submarine, which can maufacture its own oxygen from sea water to replenish the onboard atmosphere, will be able to circumnavigate the entire globe while submerged and advanced nuclear technology means that she will never need to be refuelled.
The Minister for Defence Equipment and Support (DE&S), Quentin Davies, said:
"This is a significant milestone for Astute as she sails for the first time towards her home port of Faslane.
"The Astute Class of submarines will deliver a step change in capability for defence in terms of anti-submarine and anti-surface warfare, protecting the deterrent, and providing land attack and intelligence-gathering.
"Astute will now begin a set of sea trials ahead of her full acceptance with the Royal Navy next year.
"I would like to pay tribute to both the MOD and BAE Systems Submarine Solutions staff who have worked so hard to achieve this remarkable feat of engineering."
DE&S's Director Submarines, Rear Admiral Simon Lister, who has overseen the final stages of the submarine production and preparation for sea trials, said:
"Building a nuclear submarine is a huge challenge and demands the highest standards of design, engineering and manufacturing to ensure she can safely perform her demanding duties.
"Submarine building combines a huge variety of elements; sometimes it is more like blacksmithing, manipulating the steel of the hull, and sometimes it is like brain surgery, dealing with advanced technology and performing tasks to an almost unbelievable level of accuracy.
"Astute represents the sum of thousands of individual efforts, and everyone involved in her creation can be proud."
Measuring nearly one hundred metres from bow to stern, Astute is longer than ten London buses and, when fully stored, will displace 7,800 tonnes of sea water, equivalent to 65 blue whales. She is expected to arrive in Faslane later this week.