Ms Gray, 55, who is also an author, journalist, producer and former student at the school, said she had been appointed to the post at one of the most exciting moments in its history.
She will begin her three-year post as the chairwoman of the board of governors in December, and is joining only a few months after the school's new director, Professor Tom Inns.
Ms Gray said her role as chairwoman was to support the director and his team as well as "keep them in check" like a second chamber of a parliament.
She said: "It is a very experienced board at present, and what is most exciting, and this rarely happens, is that both the director and the chairwoman is new.
"Seona Reid (former director) has left this school in spectacularly good condition, financially, internationally, with the new building: it is a thrilling time and brilliant to join an organisation in this condition.
"I am joining at one of the most exciting and exhilarating times in its history, so it is a privilege and I cannot wait."
On the new £50 million school building, designed by American architect Steven Holl, she said: "It is exquisite, I keep watching it going up, and whenever I am in the city centre I come to see it. It is going to be beautiful."
She was a student in the academic buildings that were demolished, and added: "I can tell you they were dreadful.
"I was in the Fowlis Building, and the only good thing about it was that it looked out at the Mackintosh Building: it was a shambles.
"The Newbery Tower was appalling, an architectural jumble, but this, because it is site specific - with students in mind, with the city in mind - it will be perfect."
Ms Gray, who studied graphic design and illustration at the school, takes over from Philip Rodney, who has served as chairman for the last three years.
She served as assistant head of design at the National Museum in Edinburgh before presenting Channel 4's ground-breaking music programme, The Tube.
She then went on to run a successful television production company and has written for many publications, including the Sunday Herald, winning Columnist Of The Year in the 2001 Scottish Press Awards.
As an author Gray's works range from horror fiction to the history of Kelvingrove Art Gallery and Museum.
Professor Inns said: "Muriel Gray has made a hugely important contribution to the cultural life of Scotland as a writer, broadcaster and businesswoman, and is already a great inspiration to our students.
"Since graduating Muriel has always been generous with her time, supporting the institution in many ways.
"Most recently she served as vice-chairwoman of the international jury that selected Steven Holl as the architect to design the school's new building, and she is a member of the development trust for phase two of our Garnethill campus development."
Ms Gray's appointment will be initially be for three years.
She said she attended the school at the same time as the Scottish actor Peter Capaldi: "One of us is Dr Who and one of us is chairwoman of the art school, so that's not bad."
Ms Gray said she was also responsible for building the Vic Cafe at the school, having found its interiors in a skip in the south side of the city.
She is the author of five books, three best-selling novels and two non-fiction, plus many short stories and essays published in anthologies, was chairwoman of the judges for the 2007 Orange Prize for Fiction, and serves annually on both the Bafta and the Royal Television Society awards juries.
Ms Gray is a former rector of Edinburgh University and has been awarded honorary degrees from the Glasgow School Of Art, Glasgow University and the University Of Abertay.