The grant from Glasgow City Council will go towards a third cinema screen, improving disability access and customer services and relocating the existing catering facilities.
The decision had cross party support and was agreed by the Council’s Executive committee.
The committee heard the GFT was "bursting at the seams", often stopping a film’s run despite high income at box office.
The lack of space was also affecting the cinema’s ambitions for the Glasgow Film Festival, which currently has a revenue return of £7.85 for every £1 invested.
The new third cinema screen, expected to be open at the end of 2013, will help the GFT meet these demands.
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1500 new programming slots a year are expected to be created by the expansion, amounting to a 50% increase.
GFT says the first six months of operation should allow for an additional 16,800 admissions.
2014/15 will be the first full year of operation, during which time GFT will allocate 300 out of the 1500 new slots at the theatre to non-cinema activity, including youth group meetings, extended talks and debates and private hire.
Councillor Gordon Matheson, Leader of Glasgow City Council, said: "Glasgow is a city that has long been in love with the movies. It is a love affair which has helped turn our city into the centre of Scotland’s film and television industry.
"However we have to ensure that we continue to support and give a platform to new talent coming into these industries. This is a vital part of the work of the GFT which is one of the UK’s most successful cinemas."
Bailie Liz Cameron, Chair of Glasgow Film, said: "We are delighted with this announcement and would like to express our thanks to Glasgow City Council. With admissions to GFT of over 200,000 in the financial year 2011–12, our two cinemas welcome more than twice the UK screen average admissions."
(IT)
