All 12 statues, including the 78ft Scott Monument in the centre of the Square, will be taken down and their plinths removed.
They will be put into storage and restored while a decision is made about their future.
A council spokesman said: "A tender is being prepared about moving the statues to allow us to undertake a conservation programme on them."
The statues will be taken out to allow work to begin on the £15million transformation of the civic heart of the city.
Only the Cenotaph will remain and it will be kept under wraps to ensure it is not damaged during construction work.
More than 100 architectural firms from around the world expressed an interest in designing a new Square and 35 submitted formal bids. They are expected to include a wide range of dramatic designs.
A shortlist will be drawn up and the public will be asked next month to vote for their favourite scheme.
The first phase of the plan, which will see most of the new-look Square completed, will be finished in time for the Commonwealth Games in 2014.
The future of the statues will depend on which design is chosen.
Some people want them returned to their traditional home in front of the City Chambers, but others believe they will be better in other parts of the city, including parks.
Demonstrators against the changes marched from the Donald Dewar statue at the top of Buchanan Street to the Square last night. The Glasgow Defence Campaign believes the Square should be kept as a place for protest.
DESIGNERS were told the revamped Square must celebrate the creativity of the city and its people and must create a day and night environment.
It must also be suitable for large and small activities, be of outstanding quality and create a world class tourist destination.
Council leader Gordon Matheson made it clear he wanted the red surface removed and has asked designers to consider plans for a dramatic water feature in the area.
Lighting will also play a big part and designers have been told to think big when coming up with lighting plans.
A report to councillors said: "There is a once in a generation chance to deliver a world class lighting design that turns the extraordinary into the breathtaking.
"The lighting design should be spirted and bold. It should be animated and should respond to the various users of the Square, for example, gently glowing as office workers cross the Square in a drizzling cold winter evening or dazzling and vivid as thousands fill the Square for a concert.
"The lighting design should be refined and elegant during civic events or vibrant and playful for Christmas and the wider festive season."
Mr Matheson said: "We have an opportunity to create a square of international significance we can be truly proud of.
"We received over 100 expressions of interest from more than 10 countries, including Australia, America, Spain and all four Scandinavian countries."
A spokesman for Historic Scotland said: "We are considering an application by Glasgow City Council to temporarily remove the statues and will be discussing the detail of the proposal with them.
"We will also be happy, if asked, to advise on conservation measures for the statues."
GEORGE Square was laid out in 1782, but it was during the 19th century that statues were erected to mark the greats of Glasgow, Scotland and Britain.
They include poets, soldiers, adventurers, scientists and local and national politicians, as well as Queen Victoria and Prince Albert.
The statue of Glasgow-born General Sir John Moore was erected in 1819.
He was elected to Parliament as the member for Lanark Burghs and fought in Spain against Napoleon.
In 1832, it was followed by the statue of Greenock-born James Watt. He developed the steam engine, which spurred the industrial revolution, while working at Glasgow University.
The statue of Edinburgh-born novelist Sir Walter Scott was erected in 1837 and Queen Victoria on horseback followed in 1854.
The statue of Conservative Prime Minister Sir Robert Peel was erected in 1859 and in 1866, Prince Albert's statue joined his wife's in the Square.
Next up was Glasgow-born Field Marshall Lord Clyde, a hero of the Crimean War. He arrived in the Square in 1868.
Brilliant chemist Thomas Graham, who was a Glasgow University graduate, had his statue erected in 1872.
The monument to James Oswald, one of Glasgow's first MPs, was unveiled in 1855.
And the statue of Scotland's national poet Robert Burns was put up in 1877, the same year as that of Glasgow-born poet and journalist Thomas Campbell.
The most recent monument dates to 1902 and honours four times Prime Minister William Gladstone, who was born to Scots parents.