The firm has paid £4m for McLaren’s 50% stake in the scheme.
Resolution to grant planning consent was secured in September 2014 to transform a derelict fruit and vegetable market into a mixed-use regeneration project.
Circus Street will incorporate 142 residential units, 450 student beds, 38,000 sq ft of office space as well as a new dance studio for South East Dance and a new library and academic buildings for the University of Brighton.
The project is being delivered as a public private partnership alongside the freeholders of the land, Brighton and Hove Council and the University of Brighton.
Construction on the site is expected to start later this year.
Matthew Weiner, Executive Director said: “Circus Street will create an exciting new quarter within Brighton, offering first class facilities for the University and for South East dance within a vibrant new mixed-use community.
“Originally one of the projects within Cathedral Group’s portfolio, Circus Street perfectly complements our activities and builds on our experience in mixed-use regeneration in Greater London and the South East.
“We look forward to delivering the project alongside the Council and the University of Brighton.”