Work will transform a two acre site which was a former Royal Mail sorting office.
Construction information specialist Glenigan said that Vinci has been awarded the deal by developer Barberry.
Barberry is working in partnership with Coventry University on the Bishop Gate scheme which will provide 1,116 student beds across five tower blocks rising up to 17 storeys.
Arcadis is acting as cost consultants, with Hoare Lea as M&E engineers, Nolan Associates as Civil & Structural engineers, Bilfinger GVA as Planning Consultant and Stride Treglown architects.