Workers from Dem-Masters are now on site emptying out the B-listed venue that is to be converted into a 10-storey office and retail block.
Campaigners launched a bid to rescue the space, which drew interest from music show producer Sir Cameron Mackintosh.
Steven Raeside, of the Scottish Preservation Society, had battled to try and save the building, which he believes to be the last large cinema and music hall of its type in the UK.
Mr Raeside said: "It is a real shame to see this building go, not only because of its architectural significance but because so little was done to try to save it.
"Losing this building should be the final stopper. It should be the point where Glasgow begins to realise what it has lost and not risk any more of our buildings."
The former Odeon cinema and Paramount music venue, which originally opened in 1934, played host to some of the biggest stars of the day from the Beatles to the Rolling Stones and Cliff Richard.
It was sold as part of a £60million development plan that will see most of the building knocked down, save for the Art Deco facade and foyer area.
In April last year the Evening Times told how Sir Cameron hoped to turn the former cinema into a theatre and had commissioned colour sketches of how it could look.
At the time he said: "The last large auditorium is the old Odeon.
"I have come up with a scheme where you could put a wonderful 2000-seater there, but the city doesn't seem to want it. I would certainly contribute money towards it."
The 2800-seat venue, originally called the Paramount, became a landmark with its art deco lobby and white granite curved facade. It closed in 2006 and has lain empty since the last film was screened there.
The demolition work follows a deal between owners Duddingston House Properties, and developers Mountgrange and PRUPIM, who have bought most of the building.
Demolition is expected to be completed by the end of this year, and the 143,000 sq ft of Grade A office and retail space expected to be completed by December 2014.