The 7,500 sq m six-storey building will be developed in a campus location opposite the Shorehead roundabout between Queensgate and Wakefield Road in Huddersfield town centre.
The building will provide a new home for the university's Law School and the School of Music, Humanities and Media.
It will also link the university's Student Central Building, which was completed in January 2014, at a cost of £22.5 million.
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Chris Brown, Operations Director at Morgan Sindall's Leeds office, said: "This is a key building for both the university and the town. It is a fantastic project to be involved with and our appointment builds on the existing relationship we have with the University of Huddersfield.
"We very much look forward to getting on site and creating this amazing building which will mark Huddersfield out as a forward-thinking town."
Upon its completion in 2017, the building will provide new teaching space including large tiered lecture theatres.
The development was granted planning consent by Kirklees Council in April 2015.
Vice-Chancellor, Professor Bob Cryan said: "We are delighted to be working with Morgan Sindall on the latest major development to our campus."
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