Audit Scotland will home in on the fiasco as part of its annual check on the quality of the council's management.
The watchdog said the council's external auditor "recognised the concerns that have been expressed about the governance of the George Square project" and factored it into the 2012-13 audit.
The move, which is a further blow to the city's beleaguered Labour leader Gordon Matheson, was prompted by a complaint from Glasgow's sole Tory councillor, David Meikle.
He asked Audit Scotland to investigate after a design competition ended in farce in January.
Despite the £15 million overhaul of George Square being a Labour manifesto promise at last year's council elections, Matheson announced that the project was being scrapped just minutes after a £100,000 judging competition picked the winning design.
Despite insisting for months that there was public backing for the changes, Matheson said the scheme was being axed because of public opposition.
He said the square would get a modest "facelift" instead of the transformation proposed in architect John McAslan's winning design.
The Sunday Herald later revealed that Matheson had made himself chairman of the judges, opposed the McAslan design from the start, and had wanted a rival scheme by architects Burns + Nice to win.
When the other judges ranked McAslan first and London-based Burns + Nice fourth, Matheson "threw his toys out the pram", according to council sources.
Now, in a letter to Meikle, Audit Scotland has confirmed its interest in the affair. "The George Square project is one of a number of factors that we will consider in forming our opinion on governance within the council as part of the annual audit for 2012-13," it stated.
"The way the council handles proposals for major capital investment is an important issue in our audit work. Project appraisal is vital to support that investment.
"It is important, however, that the appraisal process is transparent and that any decisions that are taken are subject to appropriate levels of scrutiny and approval."
The findings are expected later this year.
Meikle said: "I'm delighted Audit Scotland are looking into the George Square debacle. I think Glasgow taxpayers will be equally pleased that the mismanagement of public money is being examined in this way.
"I hope the development now prompts Councillor Matheson to reflect on his role and apologise to the public for the gross mishandling of the affair."
SNP opposition leader Graeme Hendry added: "I welcome Audit Scotland looking under the surface to see if best value was achieved."
The George Square design row came just days after it emerged that Matheson had been reported to prosecutors by police for an alleged public sex act in a car with another man near his home. No action was taken after prosecutors concluded there was "insufficient evidence" of a crime.
Matheson later apologised to his civil partner, Stephen Wallace, for having "an affair".
The back-to-back controversies prompted Matheson's critics within the Labour Party at the City Chambers to discuss ousting him at their annual general meeting in May. However, so far no credible contender has emerged to replace him.
A council spokesman said: "Audit Scotland routinely look at all aspect of the council's work. We will of course provide them with any assistance they require."
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