The 11-storey building is being built in Cardiff in collaboration with developer Stoford on the former David Street car park in the city centre.
Work will start on site this April and is scheduled for completion in March 2014.
Head of Property for Admiral, Huw Llewellyn said: “The new offices comply with the environment BREEAM ‘Excellent’ standard for sustainability and energy efficiency and will be tailored to our needs.”
It will feature a pale stone clad finish and large expanses of glass to maximise natural daylight on every floor.
The building will be serviced by a below ground car park for up to 120 vehicles.