They join Roxy Music singer Bryan Ferry who became a trustee of Glasgow School of Art more than a year ago.
The appeal cash will be used to help rebuild the fire-ravaged Mackintosh Building.
Firefighters managed to save 90% of the world famous building and 70% of the contents but it is estimated it could cost up to £35m to restore.
Art School director Professor Tom Inns said: "We are delighted both Peter, 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.
"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.
"The 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."
Mr Inns said the school was now beginning to look forward to the work which will need to be done to return the Mackintosh Building to its former glory as an inspiring place for students to make work.
Glasgow born Capaldi, 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."