Obama was originally scheduled to travel in March but cancelled at the last minute to stay in Washington to push for passage of a healthcare bill.
"President Obama underscored his commitment to our close alliance with Australia and our deepening partnership with Indonesia," the White House said in a statement.
"He plans to hold full bilateral meetings with prime minister Rudd and president Yudhoyono on the margins of the G-20 meeting in Canada".
The group of 20 major economies is due to meet in the Canadian city of Toronto in late June.
Oil spill concerns
Obama has called the Gulf of Mexico oil spill his "highest priority".
Americans are growing increasingly angry about the disaster, which has become the worst oil spill in history.
A series of tough political fights at home means international diplomacy may have to take a back seat to domestic policy for Obama.
The US and Australia have been long-time allies, with Australian troops serving alongside American missions in Vietnam and Iraq.
US officials are keen on keeping Indonesia, the world's most populous Muslim nation and an emerging economy, as an ally and trading partner.