The A$5bn (£2.9bn) terminal will be located in the suburb of Badgerys Creek - 50km west of the city centre.
Prime Minister Malcolm Turnbull described the development as a "vitally important project" for both Sydney and the nation.
As part of the project, the Australian government would take on the airport’s building after the operator of Sydney’s existing airport - Sydney Airport Group - declined the job citing the project’s financial risks, BBC News reports.
The decision came as a means of relieving pressure on Sydney’s Kingsford Smith airport and comes after more than 70 years since the idea was first conceived.