HMS Duncan is the sixth new generation destroyer to be Clydebuilt.
Workers lined the quayside to cheer and applaud as Duncan slowly set sail on the start of a 300-mile voyage to her new home port of Portsmouth.
She is the last of a new fleet of destroyers which has been built to replace the ageing Type 42s at a cost £6 billion.
The Type 45s guaranteed survival for the Scotstoun and Govan yards and in return the workforce produced the world's most advanced warships.
The ships' radar systems can track flights in and out of European airports in Amsterdam and Madrid from the banks of the Clyde and they are armed with Sea Viper missiles, capable of destroying enemy fighter jets 70 miles away.
The warships are the first to be produced in the UK with all-electric propulsion systems, and each can produce enough power to heat and light a town the size of Paisley.
They are also the first to offer junior ratings the luxury of sleeping in six-berth cabins.
Duncan has been fitted out in record time since her launch in October, 2010.
Programme director Jennifer Osbaldestin said: "Duncan is an outstanding vessel and we are all extremely proud to see her begin her delivery voyage to Portsmouth.
"After a very successful build period she will now become the newest asset in the fleet when she is formally handed over to the Royal Navy, joining her sister ships and completing the class of highly capable and advanced Type 45 destroyers."
The Royal Navy has appointed James Stride as the commanding officer of the ship.
Captain Stride said: "HMS Duncan is a fantastic ship, offering a world-class air defence capability, and as we leave the Clyde I can reflect on the hard work from everyone involved in the build programme to get us to this moment.
"My team are all very keen to take full custody of the ship once she gets into Portsmouth and starts her training and trials prior to deploying around the globe, protecting our nation's interests."
And Duncan maintained an old Clyde tradition by blasting its horn to salute war veterans as she sailed by the site of the old veterans' hospital at Erskine.
The destroyer is due to reach port on Wednesday where Duncan will be handed over to the Ministry of Defence before the warship is almost immediately commissioned into the Royal Navy.
The ship could spend another year undergoing sea trials before the crew of less than 200 are battle ready for their maiden voyage.