A hotel extension and office block will be removed to make way for expansion of the station to accommodate longer electric trains.
The complex, which handles some 20 million passengers a year, will stay open during the transformation, which is due to be completed in 2020.
The overhaul will include a new glass frontage onto George Square - a view blocked since the 1970s by an extension of the Millennium Hotel.
The addition, built on pillars, will be demolished, along with the adjacent Consort House office block, built around 1975, which housed Strathclyde Partnership for Transport until 2016.
Excavators have been lifted by crane onto the 30m-high (100ft) roof of Consort House to break up its reinforced concrete and steel frame, floor-by-floor.
The ScotRail Alliance with Network Rail said the work would improve Glasgow’s cityscape.
Managing director Alex Hynes said: “The first thing we have got to do is get rid of these horrid buildings, which were built in front of this listed train shed [covered station].
“Consort House is not one of Glasgow’s prettiest buildings.
“This is going to be amazing for Glasgow - it’s going to bring the railway into the heart - to George Square.”
Network Rail said the station’s roof had protected listed status as the only remaining large single span at a Scottish station.
It was constructed in 1880 by the North British Railway Company as an addition to the original 1842 station, amid competition with the rival Central Station, which had been expanded in 1879.
A new fleet of electric trains are due to start operating on the main line to Edinburgh from Queen Street from late next month.
Some are due to be lengthened to eight carriages - compared to the current maximum six - by the end of the year.
The fastest journey times are also due to be cut by ten minutes to 42 minutes at the same time.
However, the alliance said today that that depended on a separate scheme to electrify the line to Dunblane being completed on time, as its trains share part of the main Edinburgh-Glasgow route.