Eastwood MSP, Jackson Carlaw, led the tributes after hearing the news.
He said: “It was a pleasure to work with Allan Stewart, who has sadly died this morning, during his 18 years as MP for East Renfrewshire between 1979 and 1997 and in the years after during which he remained a staunch supporter and campaigner.
“As the last man to have won Eastwood for the Conservatives, I had Allan very much in mind when I was able to secure Eastwood again for the Scottish Conservatives in May.
“Allan served as a Scottish Office Minister under both Margaret Thatcher between 1981 and 1986 and John Major between 1990 and 1995. He had a considerable influence on policy during those years and was a strong supporter of both Prime Ministers.
“It was thanks to Allan that Eastwood remained outside of Glasgow during local government reorganisation, instead becoming part of the new East Renfrewshire Council.
“At the 1992 General Election, Allan achieved the largest swing to the Conservatives by an incumbent MP anywhere in the UK, something of which he was immensely proud, before retiring, undefeated, in 1997.
“I certainly benefitted from his advice on many occasions over the years and will miss him enormously.
“At his side throughout was Susie and we send our thoughts and all best wishes to her and to their children Jack and Rosa.
“Funeral arrangements will be advised in due course.”