The project will feature wet laboratories, interactive spaces for students and a student services and administration centre, as well as an atrium linking it with the nearby Biomedical and Natural Sciences building.
Enabling works started on site in July 2015, and the project is due to complete in autumn 2016.
The University of York has undertaken significant redevelopment in recent years, investing in 20 new buildings on the original Heslington West campus, and undertaking a £750 million campus expansion at Heslington East, to accommodate some 16,000 students and 3,500 staff.
John Gittins, divisional director at Interserve, said: “We are looking forward to building a long-term relationship with the University of York as it continues to invest in world class facilities to attract the very best students, researchers and staff.
“Securing this first project with the University highlights Interserve’s growing presence and expertise within the buoyant higher education sector and extends our relationship with the Russell Group, for whom we are currently working for on six universities in the north.”
The university is part of the Russell Group of UK universities, which is committed to the highest levels of academic excellence in both teaching and research.
Professor Ian Graham, the head of department in Biology at York, said: “We are looking forward to working with Interserve in the development of the Bioscience Complex at York. With the doors of this exciting new learning space due to open for the start of the 2016/17 academic year we have a very busy year ahead.”