Aimed at recovering the remaining low-pressure gas from the North Rankin and Perseus gas fields, the project will include the installation of a second platform housing gas compression facilities, utilities and new living quarters.
Project start-up is expected in 2012.
"This project will extend the field life of the North Rankin and Perseus fields and will support the venture's onshore gas commitments to supply customers post 2013," Woodside chief executive Don Voelte said.
He added the development would continue to maximise the value of Australia's largest resource project.
The North Rankin B platform, with a topsides weight of about 23,600 tonnes, will stand in about 125m of water and be connected by a 100m bridge to the existing North Rankin A platform.
The project will also include the necessary tie-ins and refurbishment of North Rankin A.
Once completed, both platforms will be operated as a single integrated facility.
BHP Billiton Petroleum chief executive Michael Yeager added the approval of North Rankin B follows the approval of the fifth liquefied natural gas train at the North-West Shelf project.
The new production train being built at the Burrup Peninsula will produce 4.4 million tonnes of LNG per annum, bringing total output at the North-West Shelf up to 16.3 million tonnes per annum.