The bill was passed in both houses of the Australian parliament this week.
Asia faces an infrastructure financing gap, estimated to be worth US$8 trillion over the next decade, Australian Treasurer Joe Hockey said in a speech at the second reading of the bill in August.
"Australia's prosperity and economic growth are tied closely to the region. It is therefore important that we are involved in a major regional economic initiative such as the AIIB," Hockey said.
Australia's initial shareholding will be US$3.7bn, including US$738 million in paid-in capital, he said.
In June the Australian treasury said that Australia will be the sixth-largest shareholder in the AIIB
The AIIB was launched in Beijing last year to boost investment in infrastructure in Asia. It is expected to have initial capital of close to US$100 billion to invest in infrastructure projects. It will be financed by individual country contributions proportionate to their economic size.
Australia-based infrastructure expert Greg Campbell of Pinsent Masons, the law firm behind Out-Law.com said: "This is exciting news, particularly for our clients that are focused in the infrastructure space in the Asia-Pacific region. The Asian Infrastructure Investment Bank will play an important role in one of the fastest growing regions of the world."
Other countries set to join the AIIB include Singapore, Indonesia, Thailand, France, Germany, New Zealand and the United Kingdom.
Infrastructure expert Simela Karasavidis, also of Pinsent Masons, said that Australia's economic growth is closely tied to the Asia-Pacific region.
"By boosting infrastructure investment in Asia, this will in turn benefit Australia and other countries situated in the Asia-Pacific region, creating a greater demand for Australian commodities and for specialist know-how and experience in the construction of major projects. Importantly, improved infrastructure will stimulate economic development in the region, further boosting trade, business and construction opportunities," Karasavidis said.