The company he founded in the 1950s, Arnold Clark Automobiles, announced he had died peacefully at home on Monday.
It released a statement saying it was saddened to announce the passing of its founder and chairman.
The statement said: “Sir Arnold was a truly inspirational business leader and influential public figure.
“His unsurpassed work ethic and strong family values led him to build a market-leading automotive retailer that continues to go from strength to strength. Sir Arnold's entrepreneurial ideals continue to be at the heart of the business.
"His personal philosophies will continue to inspire everybody who works in the business, and will be the cornerstone of its future growth and continuing success. Our thoughts are with his family at this difficult time."
His family also released a statement.
It said: “Sir Arnold Clark passed away peacefully surrounded by his family. He was a beloved husband, father, grandfather and a great friend and employer to many.
"He was an inspiration and the family will continue to carry on his vision. He will be greatly missed.
"We wish to thank all those who have sent messages of condolence and appreciate your kind support. We ask for privacy at this difficult time to allow the family to grieve."
He founded the dealer group after completing his service in the Royal Air Force, opening his first dealership in 1954.
He is said to have used his ‘demob money’ to buy a Morris Ten Four for £70, before restoring it and selling it on for a profit.
He soon opened the first Arnold Clark showroom in Glasgow’s Park Road, going on to establish hire car schemes, repair centres, franchises and a car finance and insurance business over the next decades.
Sir Arnold was knighted in 2004. Adding to his knighthood, awarded by the Queen, and numerous business honours, Sir Arnold also collected an honorary degree from the University of Glasgow in 2005.