McCoist was already a hero at Ibrox when Gazza joined in 1995 with the pair spending three years together at the Scottish Premiership giants.
Smith was in charge at the time though the trio only met for the first time while in America's famous 'Sin City'.
And McCoist admits the boss may have immediately regretted his decision to sign Gascoigne following the events in Vegas.
"The first time I met him, honest to God, was before he even signed," McCoist revealed on talkSPORT.
"We knew he was signing but he was on holiday is Las Vegas, and I was in Vegas too, and so was Walter.
"Walter said to us, 'I'll take you for lunch', so we arrange to meet in this hotel, it might have been Caesars Palace, I can't remember.
"Anyway, we go to this place and Walter is running five or ten minutes late, and by the way it was one of those places where it was all you can eat and drink for $50!
"So Walter walks in, Gascoigne and I have already started, we're battering into it, chicken wings getting flung about, glasses of wine, the whole shooting match.
"And, we're surrounded by TV screens. There was racing from every racecourse in the planet, there was baseball, there was football, you could bet on everything!
"And I can still see Walter's face as he walked in.
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"Gascoigne and I are sitting at this bar watching sport – globally – while tucking into chicken wings and having a Michelob…
"Walter was like, 'oh no, what have I created? I've created two monsters here!'
"And from there on I had a fair idea Gazza and I would get on OK."
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