"The Australian government congratulates Iraq's new President Jalal Talabani and Deputy Presidents Adil Abd al-Mahdi and Shaikh Ghazi al-Yawir on their historic election," Foreign Minister Alexander Downer said.
"Through the election of this three-person Presidency Council, including a Kurd, a Shia and a Sunni, the Transitional National Assembly has shown its maturity and commitment to a united, democratic, and non-discriminatory future for Iraq," he said.
Gulf Arab states welcomed the election but urged Talabani to safeguard Iraqi unity.
Iraqi Kurds celebrated Talabani's
election in the streets of Kirkuk
The Gulf Cooperation Council, which groups six countries, urged support for the "stability, sovereignty and territorial integrity of Iraq and non-interference in its internal affairs".
In Qatar, the cabinet called for Iraq's "independence, sovereignty and territorial integrity" to be respected, official media reported.
UN Secretary-General Kofi Annan also welcomed the choice of Talabani as Iraq's first freely elected president.
"The secretary-general congratulates Mr Jalal Talabani, as well as Shaikh Ghazi al-Yawir and Mr Adil Abd al-Mahdi, on their election today by the Transitional National Assembly of Iraq as president and vice-presidents of Iraq," a statement from Annan's spokesman said.
Iraqi Kurds on Wednesday greeted the news of election of the country's first Kurdish president with celebrations, parading in the streets of Sulaimaniya and Kirkuk.
Sulaimaniya is Talabani's hometown and the headquarters of the PUK, the Patriotic Union of Kurdistan.
Despite opinion polls showing most Australians oppose Prime Minister John Howard's February decision to send 450 troops - in addition to 900 already in Iraq - to train Iraqi forces and protect a Japanese military contingent involved in humanitarian work, Downer reaffirmed Canberra's commitment to remaining in Iraq.
"We look forward to working closely with the new Iraqi government and are fully committed to assisting the Iraqi people"
Australian foreign minister
"We look forward to working closely with the new Iraqi government and are fully committed to assisting the Iraqi people," he said.
"Iraq faces many challenges, not the least of which is writing a new constitution, but Australia, and Iraq's many friends, will remain steadfast in our support."