Serco, which runs HMP Doncaster, Marshgate will manage the New Grafton Correctional Centre in New South Wales once it is built in 2020 and then for the next 20 years.
The prison will include a 1,000-bed male maximum security facility, a 300-bed female maximum security facility, and a 400-bed male minimum security facility.
Serco is part of the NorthernPathways consortium which will design, build and operate the prison for the New South Wales government.
As well as HMP Doncaster, the firm already manages jails in New Zealand, Australia and the UK including HMP Thameside.
Rupert Soames, group chief executive of Serco, said: "The contract award for NGCC clearly marks a further important expansion of our international justice business and by total contract value it also represents Serco's largest ever contract."