Australia and Indonesia say they will begin co-operating on a new security pact and a range of development issues.
Mr Yudhoyono and Mr Howard hailed a new era in mutual relations
Indonesian President Susilo Bambang Yudhoyono, who is visiting Australia, said the deal was "the most significant landmark" in their relations.
Ties soured when Australia stepped into a row in 1999 over the secession of a former Indonesian province, East Timor.
Australian Prime Minister John Howard said December's tsunami disaster had brought the neighbours closer together.
Australia played a major role in aid efforts after the tsunami, which was triggered by an earthquake and killed some 300,000 people across the Indian Ocean, most of them in the Indonesian province of Aceh.
Nine Australian troops were killed in a helicopter crash last week while on a relief mission following a smaller earthquake on the Indonesian island of Nias.
Mr Yudhoyono's talks with Mr Howard are expected to cover the issues of counter-terrorism, development and post-tsunami reconstruction.
His visit marks only the third time an Indonesian leader has visited Australia in the last 30 years, the BBC's Sydney correspondent, Phil Mercer, reports.
Mr Yudhoyono said the two countries had agreed "to have a positive and constructive cooperation in the field of defence and security."
But he did not say whether Australia had pledged it would not carry out a pre-emptive strike on militants in Indonesia if its interests were threatened.
Canberra claimed the right to attack its neighbour after the death of scores of its citizens in bomb attacks blamed on Muslim militants on the holiday island of Bali in 2002.
An earlier accord between the two countries collapsed after Australian troops stepped in to curb pro-Jakarta militias in East Timor, which had recently voted to secede from Indonesia.
Mr Howard assured Mr Yudhoyono Australia would not support separatist struggles in the Indonesian territories of Aceh and Papua.
"Australia fully respects the territorial integrity of the Indonesian republic," he said.
Mr Yudhoyono in turn pledged to back Australia's efforts to strengthen ties with east Asian nations.
He said he would argue for Australia to be admitted into a trading bloc of countries in the region - a move opposed by some key players such as Malaysia.
Malaysian Prime Minister Abdullah Badawi is expected to visit Australia later this week.