Short answer: Private developers, but there are government initiatives that can assist.
Long answer: According to the Australian Government, private developers cover all costs of wind farms, including environmental assessments, construction, decommissioning and recycling. To ensure taxpayers are protected, the government requires financial security (such as a bank guarantee) from the developer to ensure the costs and expenses related to offshore infrastructure liabilities, such as cost of decommissioning are paid by industry and not by the government.
The Australian Government’s green bank, the Clean Energy Finance Corporation, provides investment to wind farms and the Capacity Investment Scheme provides revenue underwriting for wind and solar.