The new development will include new retail space, bar and restaurant facilities and the work will focus on extending to the north and east of the existing development.
The enlarged centre will extend over the railway lines of Queen Street Station and will also be developed over the malls's existing car park.
The development contract has been awarded to the Buchanan Partnership, a joint venture between Land Securities and Henderson Global Investors.
The planning consent is subject to approval by the Scottish Government. It is expected to be approved in the coming months.