Born in Edinburgh, Fairweather spent 34 years in the army, rising from the rank of private soldier to colonel.
A major fundraiser for military charity Combat Stress – which help ex-servicemen and women – he died at the Western General on Friday.
Fairweather was second-in-command of 22 SAS men at the Iranian embassy siege in London in 1980.
His last job in the military was at Edinburgh Castle, where he was military security officer for the Edinburgh Tattoo.
In 1994 he was appointed Chief Inspector of Prisons for Scotland and held the job until 2002. He was made a CBE in 2003 for public service.
First Minister Alex Salmond led the tributes: “It is very sad to hear of the death of Clive Fairweather and my sympathies go to his family and friends. He had a fund of extraordinary stories about his time in the SAS, was always excellent company and worked hard for the public good in Scotland.
“As Chief Inspector of Prisons he brought to the job a unique combination of humanity and common sense which demonstrated how an enlightened prison regime would operate in the public interest.”