The Edinburgh-born man, who led the SAS raid on the Iranian embassy siege and spent 34 years in the Army, rising from the rank of private to colonel, died at the Western Infirmary in Edinburgh on Friday.
He leaves widow Ann and son and daughter Nick and Charlotte, who are organising a "small, private family funeral".
Services charity Combat Stress, for which he was chief fund-raiser in Scotland, credited Mr Fairweather with putting it on the map.
Trevor Royle, the Scottish committee chairman of the charity, said: "Not only did he raise lots of money for the charity but much more importantly he raised public consciousness about the whole problem of service personnel suffering from PTSD (post traumatic stress disorder).
"He raised the profile of the charity immeasurably. I've been a trustee for four years and in that time it was a Cinderella charity and now it is one of the major military charities in the UK.
"Clive was indefatigable in the way he went about the work. It helped he knew lots of people in Scotland and it helped he had a very high public profile."
During his military career Mr Fairweather completed three tours with the SAS and was also security adviser to the Iranian and Jordanian Royal Households. He was second-in-command of 22 SAS at the Iranian Embassy siege in London in 1980.
His last job in the military was military security officer for the Edinburgh Military Tattoo.
He was Chief Inspector of Prisons for Scotland from 1994 until 2002.