Sir Albert, who was affectionately known as the Buchan Bulldog for his tenacious defence of the North Sea fishing industry, died peacefully early this morning, his family confirmed.
He had celebrated his birthday on New Year’s Day.
Sir Albert represented Aberdeenshire East from 1979 to 1983 and Banff and Buchan from 1983 to 1987, when he was beaten at the polls by former First Minister Alex Salmond.
Mr Salmond, now MP for Gordon, said Sir Albert, who lived in Mintlaw, would be “much missed”.
He said: “I am sorry to hear of the passing of Sir Albert McQuarrie.
“Sir Albert was my predecessor in Banff and Buchan constituency before 1987.
“He revelled in his title of the ‘Buchan Bulldog’ and we enjoyed some fierce political debates, as worthy opponents should.
“He will be much missed, obviously friends and family, but also the wider political and public life in Scotland.”
Ruth Davidson, leader of the Scottish Conservatives, said she was “saddened” by the news of Sir Albert’s death and recalled how he was still out campaigning ahead of the last General Election in his mobility scooter.
On Twitter, she said he had been “a tremendous servant to our party, and to the North East. His ‘Buchan Bulldog’ spirit evident his whole life - out campaigning at the General election on his mobility scooter. The thoughts of the whole party are with Rhoda and family.”
Sir Albert had backed Ms Davidson as leader of the party, saying she had the ability to lead the party back to its “former glory”.
Sir Albert was credited with improving working conditions of fisherman, chiefly through his private member’s bill which led to the Regulations in the Safety at Sea Act 1986.
The legislation introduced several safety regulations for vessels, including appropriate lifejackets for all boats, automatic release life rafts and mandatory radio beacons.
Sir Albert said he had been “very proud” of his achievement for the people of his constituency.
Sir Malcolm Rifkind, former secretary of state for Scotland, described him as a “great champion of the fishing industry of the north-east”.
Despite his ties to Aberdeenshire, Sir Albert was born in Greenock and served as a town councillor between 1949 and 1966.
He also served as an officer in the Royal Engineers during WWII and attended the Royal College of Science and Technology, now Strathclyde University, where he studied the building industry.
Sir Albert received his knighthood in 1987.
Dr Eilidh Whiteford MP (SNP, Banff and Buchan) said: “I am sorry to learn of Sir Albert’s passing. After leaving public office he continued to play an active role in his local community until very recently, and will be much missed.
“My condolences are with his family and friends at this difficult time.”