The part six, part seven-storey building will include 228 en-suite bedrooms within its 29 'cluster' apartments and will be built at the University's Brownberrie Lane campus.
The development was granted planning permission by Leeds City Council's planning committee in April 2015.
The apartments will each share communal facilities such as kitchens and living areas.
The building itself will be developed within a newly landscaped environment, which will involve planting and improving pedestrian access routes.
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Each level of the building will include one seven-bedroom, one six-bedroom and three nine-bedroom clusters.
A reception area, laundry, coffee lounge and games room will be located on the ground floor.
Two warden's apartments and 13 disabled access rooms will also be included.
Chris Brown, operations director at Morgan Sindall's Leeds office, said: "This is an important appointment for us and plays directly to our strengths and experience within the student accommodation market.
"The building has been designed to raise the quality of student accommodation at Leeds Trinity University and we are committed to driving the same level of quality through the construction programme."
Stephen Oddy, Director of Facilities at Leeds Trinity University, added: "The appointment follows a welcome increase in student applications at the University over recent years. Currently there are approximately 3,200 students on campus, with an estimated 1,000 additional students expected to join over the next five years."
The contract began in August and is expected to be complete by September 2016.
(LM)
