The Greek-born Australian has been chosen to lead the Bhoys forward following a protracted 106-day hunt for Neil Lennon's replacement.
Postecoglou, however, will not be there to greet them on their first day back - with the 55-year-old now preparing for a 10-day stint in quarantine on his arrival from Japan, where he has been coaching J-League outfit Yokohama F. Marinos.
His appointment has raised eyebrows with many people, who view it as a huge gamble.
But Strachan, who managed Celtic from 2005-2009, insisted that those around Parkhead are righly 'excited' at the arrival of Postecoglou, who has been appointed on an initial 12-month rolling contract
"Everybody is overreacting as usual," the Scotland legend said. "The fact is that Ange, who's coming in, if you actually look at what he does and the people who have worked with him, you're talking about a top manager here.
"There's no point in asking pundits because they've never watched him play, they've never seen his training, they've never seen his teams, they've never spoke to his players. Ask the players who have worked with a coach what he's like, then you'll find the truth.
"I think that Celtic people are excited about this.
"I've always said, if you ever get the chance to be Celtic manager, take it. When the crowds get back, you're getting some of the best nights in European football. It doesn't get any better.
"I'm sure he'll be a success. I'm excited to get somebody who's outside the box, and not just a name that we regularly see.
"I want to see new people in front of a camera, I want to see knew training methods - and I think that's what we're going to get."
Postecoglou labelled his appointment as 'one of the greatest honours in football' after it was confirmed on Thursday morning.
He said: "The opportunity that has been given to me is one of the greatest honours in football and the responsibility to lead our magnificent football club into the future is one that I will cherish dearly.
"Celtic is one of 'the' names in world football, of that there is no doubt. A giant of a club, a proper footballing institution and so much more - real history, real substance, real authenticity and real soul.
"I know Celtic is a true way of life for so many people and I know the demands which come with this position - I am ready to do all I can to meet those demands.
"I will be doing everything I can to get our great club back on top and, at the same time, deliver the kind of football which our fans appreciate. We want to entertain our fans and we want to win, these are the objectives which I always set myself and which I now begin work on."
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