Local people watched as the ship sailed up the Clyde yesterday passing the Erskine Bridge, Titan Crane and Braehead and Scotstoun.
She finally berthed at the King George V Dock, down river from Govan, where she was launched, and across from the Scotstoun yard where she was fitted out.
She is the second of a new generation fleet of six Type 45 destroyers which were built in the Glasgow yards owned by giant defence contractor BAE Systems.
The last Type 45 to visit the city was sister ship HMS Defender.
Defender is the only Type 45 officially twinned with Glasgow.
HMS Dauntless will be in port until Monday but is not open to the public, though she will play host to school children, cadets and VIPS. A series of onboard visits have been arranged involving Glasgow pupils.