Under the Deeley Freed plans the shopping centre’s car park will also be demolished.
Councillors voted unanimously to approve the plans, which include offices, 450 homes – 90 of which will be classed as affordable – and student flats which can accommodate 750 people are also part of the project.
Max Freed, director of Deeley Freed, said: “The Galleries has been struggling since well before the pandemic.
“It’s poorly designed and car parking covers 40% of the site. It has long been obsolete. Our proposal would completely transform the site.
“There would still be shops and restaurants on the ground floor throughout the development, including new units facing outwards to Castle Park and Broadmead.”