The 100,000 sq ft, seven storey building will be located at the city centre campus in Charles Street
The council initially gave planning permission for the building in 2010, but the university revised the design.
The building is presently out to tender with an estimated build cost of £19m. If planning is approved, construction should start later this year, with completion expected in 2015.
Mark Swales, director of estates and facilities at the university, said: “This is part of a £100m investment in our estate over three years.”
Turner & Townsend is providing project management, cost management, CDM coordinator and ICT consultancy services to Sheffield Hallam University for the scheme.