The Scottish Government has provided a £20m rescue package to move the project forward.
The project, which was first granted planning over six years ago, had been delayed due to rising costs.
The landmark venue will provide a permanent home for the Scottish Chamber Orchestra and a major base for the Edinburgh International Festival.
Commissioned by IMPACT Scotland, the concert hall is a significant development for the city's cultural scene.
Author's summary: Balfour Beatty starts £162m Edinburgh concert hall job.