Leading companies from France, America and the UK will now draw up detailed plans, which will go on display in The Lighthouse in January.
The £15million redesign of George Square will involve all the monuments, with the exception of the Cenotaph, being removed.
Whether they are returned to their traditional home outside the City Chambers will depend on which design is chosen by councillors early next year.
Neil Baxter, secretary of the Royal Incorporation Of Architects in Scotland, described the shortlisted firms as "world leaders".
He said: "It is a tremendous international list that combines some very well known names with one or two wild cards and a good smattering of Scots, which is ideal for a competition for Scotland's biggest city.
"It is good we have world leaders alongside wild cards, who often come up with something that surprises you and is by far the best submission."
Mr Baxter said he was not surprised the hunt for an architect to redesign George Square had attracted such high quality interest.
He said: "In terms of international jobs, it is financially on the smaller scale.
"But in terms of prestige, being able to affect the future shape of the centre of a city is an important task and could be career making."
City council leader Gordon Matheson believes George Square is rundown and shabby and no longer fit for the 21st century.
He wants the unpopular red surface to be removed and has made it known he would be keen to see a water feature included in the winning design.
He said: "George Square's redevelopment is a hugely exciting moment in the growth of the city as we continue to drive Glasgow forward to meet its future challenges.
"The calibre of the companies competing to redevelop the Square clearly outlines how iconic it is around the world.
"Each bidder has a wealth of international experience and all six have delivered a number of eye-catching civic spaces acclaimed by their peers and public alike.
"The city attracts thousands of tourists and conference delegates every year, who generate millions of pounds for Glasgow's economy, and we need to invest in our city if we want that to continue.
"This means it is essential we choose the very best designer-led team to create a new George Square fit for the 21st century.
"I look forward to working with the winning design team and the people and businesses of Glasgow to give the city the George Square it deserves."
The redevelopment will be carried out in two phases, with the first finished before the Commonwealth Games in 2014.
It is likely the area will be shut from just after the New Year, when the bulldozers will move in to start work.
The monuments in the Square and the plinths will be taken down and conserved while their fate is being considered.
THE FIRMS WITH A DESIGN ON GLASGOW
l French company Agence Ter has worked on a wide range of international projects, including the Grand Egyptian Museum being built on the outskirts of Cairo; the Central Park Bridges at the 2012 Olympic Park, London; the Giant's Causeway visitor centre in Northern Ireland; and a library and school of architecture for Greenwich University, London.
l UK based Burns+Nice's recent public realm works include Leicester Square, London; the Millennium Quarter in St Helier, Jersey; and a series of public spaces in and around London, including St Martin's Courtyard in Covent Garden and the new precinct outside the Old Bailey and Bow Courtyard.
l Gustafson Porter, which has its HQ in London, is mainly responsible for public realm schemes. The company's designs include the Princess Diana memorial fountain in Hyde Park, London, and squares, gardens and parks in the UK and abroad. These include Old Market Square, Nottingham; Woolwich Square, London; Westergasfabriek Culture Park, Amsterdam; Parco CityLife, Milan; and Shoreline Walk, Beirut.
lJames Corner Field Operations is based in New York. Its projects include the High Line Park in New York; Queen Elizabeth Olympic Park and a redevelopment of Earl's Court, both London; the historic Navy Pier, Chicago; a new waterfront city for Shenzhen, China; a master plan for Seattle's Central Waterfront; the Race Street Pier in Philadelphia; Hong Kong's Tsim Sha Tsui Waterfront and the Civic Centre Parks in Santa Monica.
lJM Architects, which has an office in Glasgow, has recently worked on Glasgow School Of Art; Hillhead Primary School; and the redevelopment of Bonn Square, Oxford.
l UK based John McAslan and Partners' projects include the redevelopment of the Grade 1 King's Cross station in London and the Stanislavsky Factory development in Moscow.