A new version by the Royal Scottish National Orchestra, will be Scotland's victory anthem at the Commonwealth Games, played every time a member of Team Scotland wins a medal.
Folk musician Browne, 76, said the version, featuring bagpipes, was "fantastic" and urged Scots athletes and fans to sing along.
But he admitted he and his fellow Corrie, the late Roy Williamson, were stumped by its popularity.
He said: "Roy wrote it in about 1968 and it became an anthem to our concert audiences and it's just developed from there.
"I don't know why it's so popular. Neither Roy nor I understood it, but from the first time we sang it to our audiences they took to it.
"A great many people don't like it, obviously, but the way it's happened it's just grown of itself.
"Eventually football crowds and all these people were singing it."
He said it became so popular at Scotland football internationals that his vocals were overwhelmed by the Tartan Army.
He said: "About four or five years ago I performed it at 13 consecutive Hampden internationals and the crowd singing it is phenomenal.
"There's no point in me being there. You do a soundcheck with triple and quadruple echoes and then when you start with the crowd it changes itself.
"Immediately you start to sing it you'd be as well going home because they just take over, and it's fantastic to be in the middle of it."
He said he was looking forward to Scots athletes appearing on podiums throughout the Commonwealth Games, adding: "I want them when they're standing in front of that flag going up, not only for them to sing it but the crowd in the stadium singing it."