Glasgow City Council has approved the scheme, which will see the national ballet company move into a new home at the revamped and extended Tramway performance centre in the city - a decision which was originally expected almost seven months ago.
The Scottish Executive has also ratified the proposals which, the AJ understands, were initially held up due to issues with the external appearance of the development.
The project will create three large rehearsal studios, health and fitness areas, administration facilities and space for the storage of sets, wardrobe and lighting equipment.
These facilities will be housed in parts of the existing building - which will be thoroughly revamped - and in a new extension on an unused part of the Tramway site.
In addition to the money promised from the Scottish Arts Council and the National Lottery, the Scottish Ballet will now have to sell up its dilapidated home in West Princes Street to fund the scheme.
Cindy Sughrue, executive producer of Scottish Ballet, said: 'This is an important day and it takes us a step closer to realising our ambition to create a fitting home for the company at Tramway.
'We are very excited about the potential for the future, as the bespoke building will create a platform from which Scottish Ballet can fulfil its potential in so many different ways.'