The project involves modernising the derelict 1930s cinema building into a new entertainment venue.
The successful contractor for the 14-month project will be named in the next few weeks.
With a seated capacity of 3,500 and a standing capacity of 4,000, Bradford Live is expected to attract national and international performers.
The venue’s flexibility will also allow sporting events, corporate product launches exhibitions and conferences.
It will be run by NEC when it opens in autumn 2021.
T+T, which was already on board as cost consultant, will provide project management services to Bradford Live from its head office in Horsforth in Yorkshire.
Michael Grace, Director, Turner & Townsend, said: “Bradford Live will create a fantastic new entertainment hub for the city and we are delighted to be expanding our role on the project.
“With our experience working on award winning cultural projects in the region, including Leeds Play House, the Piece Hall and Yorkshire Sculpture Park’s Visitors Centre, we are well placed to ensure the successful delivery of this new venue for Bradford.”