Prime Minister Tony Abbott believes Australia can take part in a wave of confidence sweeping Indonesia under the country’s new president Joko Widodo.

Mr Widodo on Monday became the seventh president of the world’s largest Muslim population and its third-largest democracy.

The inauguration, which was attended by foreign dignitaries including US Secretary of State John Kerry and Mr Abbott, capped a remarkable rise for a softly-spoken politician who was brought up in a riverside slum.

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Mr Widodo, known by his nickname Jokowi, worked his way up through local politics before securing the presidency in July following a close race against controversial ex-general Prabowo Subianto.

He is the country’s first president from outside an ageing band of political and military figures who have ruled the world’s third-biggest democracy since the end of the three-decade Suharto dictatorship in 1998.

Mr Abbott says he’s confident he can work with Mr Widodo to strengthen the important relationship.

“I’m very encouraged by everything President Jokowi has said up to now, I really am encouraged,” he told reporters in Jakarta after witnessing the president’s inauguration.

“He’s obviously a charismatic and inspirational figure.

“I think there’s a wave of confidence and renewal sweeping Indonesia right now and I look forward to Australia’s opportunities to take part in the renewal and the reinvigoration of this important neighbour and partner.”

The ceremony in Jakarta is also a chance for Mr Abbott to farewell departing president Susilo Bambang Yudhoyono, who gave special attention to relations with Australia throughout his decade-long tenure.

The elected President of Indonesia, Joko Widodo (R) with former President Susilo Bambang Yudhoyono. Photo: AAP

When the relationship soured last year over reports Australia spied on Dr Yudhoyono’s family and friends, he eventually put personal effort into ensuring the nations reconciled before he left office.

The clean slate means Mr Abbott can at last put into action the “more Jakarta than Geneva” foreign policy style he promised when elected.

The prime minister took his seat in Indonesia’s parliament among other leaders, including US Secretary of State John Kerry who he will meet later on Monday.

Mr Widodo, popularly known as Jokowi, has already signalled his wish to become closer friends with Australia.

In a televised debate before his July 9 election win, Mr Widodo diagnosed a “lack of trust” between the nations, and perceived that Australia viewed Indonesia as the “weaker” player in the partnership.

He wants to build closer ties, particularly in security, business and people-to-people programs.

But in line with his election campaign comments, he has also warned he will be tough on the issue of sovereignty.

Mr Widodo has described as “unacceptable” the incursions of the Australian Navy into Indonesian waters during operations to turn back asylum seeker boats.

Meanwhile, the same volunteers who were crucial to Mr Widodo’s election win have organised a city-wide party to celebrate the inauguration of a man admired for his humble, small town background and known for his love of heavy metal music.

More than 150,000 Jakarta citizens are expected to turn out for a street parade, rock concert and the release of hundreds of lanterns into the night sky.