Johnstone, a Conservative member of the Scottish Parliament since 1999, had been an active member in his local parish and was a Church of Scotland elder.
He is survived by his wife Linda, two children and six grandchildren.
During his time in Holyrood he fought against same sex marriage and assisted dying legislation.
In a debate on the issue of gay marriage he told MSPs: "During my lifetime, I have seen society beginning to fall apart.
"That's why I would argue that one of the priorities of this parliament should be to strengthen families, to find ways to reinforce marriage and to make sure that we reverse the trends of half-a-century and more, in order to gain that stability."
In a statement the leader of the Scottish Conservative Party Ruth Davidson said he "embodied politics at its best".
"Alex's passing is an enormous loss for the Scottish Conservative party, for the Scottish Parliament, and for Scottish public life generally.
"He was a big man with a big heart. He embodied politics at its best: trenchant in his views, always up for a political fight, but respected and admired by all sides of the political divide for his decency and generosity."
