Leader Gordon Matheson said the city's civic heart would now undergo a substantial facelift rather than a radical redesign.
Details of the facelift are to be announced later, but it will include retaining the statues and grassed areas, and replacing the red tarmac.
His announcement came after a panel chose a winning entry in an international design contest. The jury, which had been judging six plans shortlisted in the competition, chose design number two, produced by John McAslan & Partners (UK).
However, Councillor Matheson said the council would not be proceeding with the contract.
He said: "The people of Glasgow have made it clear that they do not want a radical redesign of the square.
"They want the square to look better and be a place of which they can be proud – a place they can while away a sunny afternoon or get together and celebrate the big occasions in the life of the city.
"They also want us to keep the statues where they are, and they like the grass. However, they clearly want rid of the red tarmac.
"I am proud to say that I am listening to them.We will carry out this refurbishment work in time for the Commonwealth Games and only if there is public demand thereafter, will we consider a radical change.
"The companies which were asked to produce designs gave us stunning plans, any one of which would have looked fantastic, and I would like to thank the architectural firms involved for their time and hard work. I also want to thank the members of the jury.”
Under the procurement process for the design contest, the jury had to conclude its deliberations and choose a winner. The council would then have had to agree to award the contract. However, that recommendation will now not be put before councillors.