GSA has agreed a 95-year tenancy with Glasgow City Council which will see up to Â£20m invested in restoring the B-listed building on Sauchiehall Street.
The deal means the art school will return to the 150-year-old building, more than a century after leaving.
GSA occupied the McLellan Galleries for 30 years from 1869 before moving to its new home, the Mackintosh Building.
GSA director, Professor Tom Inns, said: "We are delighted that Glasgow City Council has approved The Glasgow School of Art as long-term tenant for McLellan Galleries.
"Our plans and investment in the galleries will bring them back to life and secure their long-term future for both the school and the city."
GSA plans to integrate the McLellan Galleries into its Garnethill campus.
Page\Park Architects has produced a series of concept ideas for the B-listed building, which include a new central courtyard and exhibition space.
There may also be a public route through from Sauchiehall Street to the art school's newly-developed precinct between the Mackintosh, Reid and Bourdon Buildings on Renfrew Street.
GSA said such a development would offer the public a glimpse into "the creative and cultural production of staff and students".
Glasgow City Council leader, Gordon Matheson, said: "The McLellan Galleries has enjoyed a great past, and now we can look forward to a fantastic future for this wonderful building.
"The Glasgow School of Art presented an extremely strong case for the long-term lease, and seem a perfect fit for the Galleries.
"This is not just great news for the development of the McLellan Galleries and the growth of the School of Art, but also for this part of the city centre."
GSA will now look to appoint architects to lead the redevelopment and then establish a timetable for the development.
The art school currently occupies the galleries, following a fire earlier this year at its iconic Mackintosh Building.
GSA will continue its occupancy, on a temporary licence, until the 95-year lease begins in September 2015.
Glasgow School of Art (GSA) is to take over the running of the city's historic McLellan Galleries.