Designed by Tim Groom Architects, the project will feature a 34-storey main block clad with black metal panels and a connected 12-storey brick envelope block.
The latest student project from Vita is planned for an already cleared site on the corner of Hulme Street and Medlock Street.
The construction management plan has been drawn up by Manchester high rise specialist Renaker.
Studio apartments will be supported by social and study spaces and a gym. An on-site operations team would be in place to provide daily events, housekeeping and security.
The new Vita Student development would be the second at First Street, with the first opening in 2014.