Dr McDonald, Moderator of the General Assembly of the Church of Scotland from 1997-98, revealed last year he was fighting the degenerative lung disease pulmonary fibrosis.
The Church said he died at the Erskine Care Home for ex-servicemen in Bishopton, Renfrewshire, on Thursday morning.
Current Moderator, the Rt Rev Dr Angus Morrison, said: “Dr Sandy McDonald was a wonderful man and minister.
“Genuine love for people was a defining mark of his ministry. He had a special concern for the well-being, at every level, of his fellow ministers. Sandy’s memory will be cherished by many.”
He is survived by three children, including the Doctor Who and Broadchurch star.
The retired minister was described by Church colleagues as a “beloved figure,widely admired for his fearlessness, generosity and irrepressible highspirits”.
In the 1980s he co-presented religious programme That’s The Spirit on Scottish television, and he once appeared with Tennant as a guest on cookery show Ready Steady Cook.
He also took on a cameo role alongside his son in an episode of Doctor Who in 2008.
Following his diagnosis, he spoke out in favour of the right to die of terminally ill people, contrary to the Church’s official position on the issue.
Colleague the Very Rev John Chalmers said: “Working with Sandy McDonald was one of the great pleasures of my career in ministry.
“It was no surprise to me when Sandy called for a serious dialogue on the right to die – he was a man who tempered his views in the light of reality, he was a man who sat lightly to dogma and who preferred faith in action.
“The Church of Scotland needs a new breed of Sandy McDonalds who catch a passion for the good news of Jesus Christ, but whose understanding of the faith is not frozen in time, but develops and matures with new revelation and understanding.”
Dr McDonald was born in Bishopbriggs, East Dunbartonshire, in 1937 and trained for the ministry after national service with the Royal Air Force.
He served at St David’s Parish Church in Bathgate, West Lothian, and St Mark’s Parish Church in Ralston, Renfrewshire, and then as general secretary of the Church of Scotland’s board of ministry until he retired in 2002.
Helen, his wife of more than 40 years, died in 2007.
Friend the Very Rev Dr Lorna Hood said: “Sandy didn’t just preach. He put his whole self into it – his arms, his voice, his whole body went into his sermons.
“People loved it when he preached. He was a great pastor and he held parish ministry at the heart of the Church.”