The Hollywood star and the Doctor Who hero are becoming trustees of the institution's appeal, which was launched yesterday.
The city and the arts world were rocked on May 23 when flames engulfed the Grade A-listed building, leading to the loss of about a tenth of the structure and 30 per cent of its contents.
Art school bosses now want to restore the structure - designed by Charles Rennie Mackintosh more than a century ago - to its former glory.
While they have already received donations and offers of support from around the world, the new Mackintosh Appeal has been established with a view to reaching the eight-figure target.
Pitt, who recently starred in 12 Years A Slave and also featured in films such as Se7en and Seven Years In Tibet, is well known for his interest in architecture and becomes one of a dozen trustees of the Mackintosh Appeal.
He is a high-profile fan of Rennie Mackintosh's work and, when filming World War Z in Glasgow three years ago, took time to visit another of the architect's designs, Hill House in Helensburgh.
Capaldi, who is a graduate of the GSA, recalled memories of his time at the art school. He said: "I hope we can come together to help raise the funds to restore the Mackintosh Building to its former grace.
"It always seemed to me, when I studied there, both as a student and as a child in Saturday morning art classes, an exotic place of the imagination ... all nooks and crannies, guarded by stern ancient statues and full of artistic possibilities.
"There is no greater symbol of the artistic spirit of Scotland than the Mackintosh Building. But more than that, it is a symbol of where art belongs, rising as it does out of the heart of a great city. A mighty castle on a hill, it is a part of me, and of all Glaswegians."
Capaldi, who also played fictional spin doctor Malcolm Tucker in the television series The Thick Of It, has recorded a special message for current students at the institution.
He said: "I'm so sorry for all of you who have lost your degree shows. All I can say to you is that you are artists. This will only add to your story. You will be reborn, and rise from the ashes even stronger."
Art School director Professor Tom Inns said: "We are delighted Peter Capaldi, one of our most celebrated alumni, and Brad Pitt, whose admiration for Mackintosh is well known, have both joined our campaign and will be trustees on the Mackintosh Appeal."
Professor Inns told MSPs at the Scottish Parliament on Tuesday that restoration of the fire-damaged building could cost £20-£35million and take up to four years.
In addition to the appeal, the GSA has set up a Phoenix Fund - to which the Scottish Government has pledged up to £750,000 - to help students affected by the fire recreate their work and recover from the setback of missing their final degree show, which would have been a major opportunity to showcase their work to galleries and collectors.
Professor Inns added: "Our priority to date has been to address the immediate physical and academic impact of the fire.
"We have been overwhelmed by the offers of support from around the world since the fire and are hugely grateful to all those people who have donated. This support, along with that of the Scottish Government, has been vital. It has enabled us to put in place the Phoenix bursaries programme to help those students who were most affected by the fire.
"We are now beginning to look forward to the work we will need to do to return the Mackintosh Building to its former glory, and to make sure it continues to be a fit and inspiring place for our students to make work."