The bill, which is expected to be signed into law by President Joko Widodo, will apply to dozens of crimes committed as far back as 18 years ago, including drug, terrorism and money laundering offences.
Indonesia's parliament has approved an extradition treaty with Singapore that will help Jakarta track down corruption suspects who have taken sanctuary or stored money offshore in the city-state.
Lawmakers passed the bill at a Thursday plenary session and it is expected to be signed into law by President Joko Widodo.
The Indonesian government is trying to retrieve billions of dollars in bailout money handed out during financial crises in the late 1990s and 2008 never repaid by suspects Jakarta calls economic criminals believed to be hiding in Singapore.
Indonesian officials have for years complained about what they say is the freedom enjoyed by fugitives in the neighbouring country where they have allegedly pumped hundreds of millions of dollars into banks and property.
"The extradition treaty with Singapore will make it easier for law enforcers to resolve a crime when the criminals are in Singapore," Justice and Human Rights Minister Yasonna Laoly told parliament before the vote.
Dozens of crimes
It will apply to dozens of crimes committed as far back as 18 years ago, he said, including drug, terrorism and money laundering offences.
The minister said the treaty was an effort to "provide justice and protection" for Indonesian citizens and showed Jakarta's "active role in maintaining the global order".
Singapore's Senior Minister Teo Chee Hean said in February he hoped the new law would help Indonesia's efforts "to prevent suspected criminals from fleeing overseas and for them to be apprehended in Indonesia".
The two countries signed a long-delayed extradition treaty in 2007 but it was never approved by Indonesia's parliament.
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