It will be Scotland's largest hospital and is anticipated to transform services in Glasgow and the west.
The new facility, given final approval by Holyrood today, will have an integrated children's and adult hospital built on the site of the current Southern General.
It will also hold 1,109 beds and provide maternity, paediatric and acute services on a single site.
Public Health Minister Shona Robison said: "Providing services for all ages on a single site will ensure patients can access the widest possible range of specialist services and will also bring with it increased efficiency, shorter waiting times and better continuity of care".
Construction of the hospital is due to be completed in January 2015 and will be fully operational by the summer.
Robert Calderwood, NHS Greater Glasgow and Clyde chief executive, said: "I am delighted Holyrood has approved the full business case for the New South Glasgow Hospitals project.
"The project will see us complete a programme of investment of more than 1.5 billion in modern healthcare accommodation across both acute and mental health facilities".