The money from the Heritage Lottery Fund (HLF) means that the £16m project to radically transform one of the jewels in the crown of the city's cultural life is now a step closer.
Dominic Hill, the Citizens' artistic director, said: "I am incredibly grateful to the Heritage Lottery Fund for their support of our ambitious plans."
He added: "Our vision for this project is to create a building which honours and celebrates the remarkable history of this theatre, while remaining a vibrant and vital landmark in our community.
"The Citizens work on stage has long been celebrated for being bold, innovative and accessible to people from all walks of life, and I'm looking forward to working in a building that reflects that philosophy.
The work would see the redevelopment of its front of house, a significant improvement of its facilities for the public, and new space for education, children, rehearsals and performances.
They are the biggest changes to the Gorbals-based theatre in 135 years and have already received up to £4m of backing from Glasgow City Council and £1.5m from the national arts funder Creative Scotland.
Further applications for grants to trusts and foundations are planned, with a public campaign to be launched during the next two years.
Work will begin on site in the autumn of 2016 and be completed by 2018, and the Citizens is planning for performances and productions to continue during the redevelopment period.
The revamp plan has been designed by Edinburgh-based architects Bennetts Associates and will overhaul the theatre's offices, backstage areas and utilities, in a design which will again reveal the original stone walls of the Victorian theatre.
The Grade Two listed auditorium will not be dramatically changed, but the steeply angled stage, which is raked on a scale of 1:17, one of the steepest in the UK, will be lowered to 1:24.
The outside of the building will feature statues of Shakespeare, Burns and the four Muses, originally from the roof of the original 1878 building, placed along its new façade.
Its archive and collection of artefacts, materials, pictures, literature, scripts and costumes will be catalogued and collected in one place, so that much of it can be accessed for the first time.
Over the years, the theatre has had actors such as Rupert Everett, Tim Roth, Gary Oldman, Pierce Brosnan, Alan Rickman and Glenda Jackson treading its boards, as well as Robbie Coltrane, Stanley Baxter, Leonard Rossiter and Moira Shearer, among many others.
The HLF grant includes an award of £500,000 to assist the Citizens in developing the project to the next stage of its funding applications process.
Colin McLean, head of the fund, said: "The Citizens Theatre is held in great affection in Glasgow and far beyond although I don't think anyone would disagree that it has seen better days.
"We are delighted to give our initial support to a project which will bring those better days back."
The listed building was opened as His Majesty's Theatre and was also known as the Royal Princesses Theatre until the building was first leased to the Citizens Theatre Company in 1945.
The theatre retains many of its Victorian features; it is the only one in Scotland still to have its original machinery under the stage and features an original Victorian paint frame and related fly system, which is still used to paint scenery.
Adrienne Scullion, chair of the theatre, said: "The Citizens has always valued its place in the heart of the Gorbals and now, with the [nearby] Laurieston regeneration project underway, it's the right time for us to invest in a more efficient, more sustainable building for future generations to enjoy."