"The change to Turnbull as leader is nice timing for the Indonesia-Australia relationship, as it will allow it to reset after it fell to a precarious position in recent years," said Greg Barton, of Melbourne's Deakin University.
"There's a feeling that the optimism within Australia, that the new leader is much more reasonable to deal with than Abbott, should also apply in our relationship with Indonesia."
Turnbull said he and Widodo had a mutual interest in growing economic co-operation.
The visit comes just a week ahead of more than 300 business chiefs and four cabinet ministers taking part in Australia's largest delegation to Indonesia. The trade visit will take to 10 the number of cabinet members who have visited Jakarta since the April executions of Myuran Sukumaran and Andrew Chan. Ministerial visits were suspended for almost four months, and the ambassador withdrawn, after the drug smugglers' executions.
Abbott's vow to relationship with Jakarta derailed when media reports revealed Australia's intelligence services had tapped the phone of then-president Susilo Bambang Yudhoyono.
- Washington Post, Bloomberg