The Indonesian leader was welcomed to Canberra with a military honors ceremony.
Yudhoyono is seen by Canberra as the most pro-Australian president in Indonesia´s history.
He is scheduled to speak before a rare joint sitting of Australia´s two-houses of parliament.
His government has chided Australian Prime Minister Kevin Ruddm, this year, for leaving mostly Sri Lankan asylum seekers stuck in Indonesian ports, while their refugee claims are assessed.
The aslylum seekers issue is clouding Rudd´s popularity in Australia.
Meantime, Rudd is pushing for presidential clemency from Yudhoyono, as a backstop for three Australian drug smugglers sentenced to death in Bali.
The three currently have appeals pending in the Indonesian courts.
Yudhoyono came to prominence in Australia after the 2002 Bali nightclub bombings, in which 88 Australians were killed.