The venue said its cafe bar, book shop, and retail space will open on Saturday.
Exhibitions and performances will restart on Tuesday.
It comes as work to stabilise the Mackintosh Building’s west gable is completed.
Art school chiefs had hoped the work would be completed by last weekend but progress was delayed by high winds.
A safety cordon has been in place in the area since the June 15 blaze, preventing access to the CCA, Bagel Mania and News 4 U.
Muriel Gray, chair of the board of governors of the Glasgow School of Art, said: “This has been a challenging time for all the residents and businesses who have been affected by the fire in the Mackintosh Building.
“We are truly sorry for the impact it has had and want to thank everyone for their patience.
“We also want to say a big thank you to all the people who have been working seven days a week since July for their commitment to get the work completed, and in particular for pulling out the stops over the last few days so that the businesses which continue to be affected by the fire can get back into their premises.”