The 7,500 square metre, six-storey building is being developed in a prime campus location opposite the Shorehead roundabout between Queensgate and Wakefield Road in the town.
The £27.5 million building will provide a new home for the University’s Law School and the School of Music, Humanities and Media.
It will also link into the University’s Student Central building which was completed in January 2014, at a cost of £22.5 million.
Around 166 tonnes of Yorkstone has arrived from Johnsons Wellfield Quarries in Huddersfield which was established as a local company in 1854.
Mark Heginbotham, project director from Morgan Sindall, said: “People will really notice a difference in the building now as we begin the installation of the stone cladding.
“Yorkstone is a fantastic material to work with. It adds a distinctive quality to the building which is one of grandeur, solidity and tradition. But here, it is not being used to create a traditional style building.
“The Oastler building is bold and modern and with its blend of traditional and modern materials, it will make a real statement in the town.”
The University’s Deputy Vice-Chancellor, Professor Tim Thornton said: “This blend of the modern and the traditional is representative of the University itself.
“This year we celebrate our 175th anniversary – and proudly celebrate the pioneers who established higher education in the town – while continuing to be at the forefront of developments to meet the needs of today’s students.”
The eye-catching building, which will provide a new gateway building to both the university and the town centre, was granted planning consent by Kirklees Council in April 2015.