Ms Indrawati's departure is likely to trouble foreign investors
Indonesia's Finance Minister Sri Mulyani Indrawati has been appointed managing director of the World Bank.
Accepting her resignation, President Susilo Bambang Yudhoyono praised her success in reforming the economy and said he would "truly miss" her.
Ms Indrawati has largely been credited with steering South East Asia's largest economy through the financial crisis.
But she is at the centre of a criminal investigation into a 2008 bank bailout, over which she denies any wrongdoing.
Analysts say her resignation will be a blow to Indonesia's efforts to tackle corruption and reform the economy.
Ms Indrawati's appointment was announced in a statement on the World Bank website.
The bank's President Robert Zoellick said she had been "an outstanding finance minister" in Indonesia and would bring to the bank her knowledge of working in a country "that still faces significant challenges of poverty".
Mr Zoellick also praised Ms Indrawati's "success in combating corruption and strengthening good governance".
Ms Indrawati will be second-in-command at one of the most influential financial institutions in the world once she takes up her new post on 1 June.
She will be in charge of three main regions - Latin America and the Caribbean, the Middle East and North Africa and East Africa and the Pacific.
In a statement accepting her resignation, Mr Yudhoyono praised Ms Indrawati - a noted economic reformer - for her achievements during her five years in office, calling her "one of our best ministers".
Protesters had called for Ms Indrawati and the vice-president to resign
"The finance minister has worked hard to develop the right fiscal policy, and to reform our finance and tax departments," he said.
"When the global crisis affected Indonesia, the finance minister worked hard to save our economy from its dire impact."
Ms Indrawati said it was "a great honour" for her and for Indonesia to "have this opportunity to contribute to the very important mission of the Bank in changing the world".
She will remain in office for another week - her replacement has not yet been announced.
The announcement comes as investigations continue into the controversial $700m (£460m) Bank Century bailout in 2008.
Parliamentarians allege that she and Vice-President Boediono were guilty of mishandling funds after some of the bank's wealthy clients later donated money to the president's election campaign.
Both ministers have consistently maintained their innocence - with Ms Indrawati saying her actions helped to save Indonesia's banking sector from collapsing.
The BBC's Karishma Vaswani says Ms Indrawati is well liked and trusted by the international investment community, so her resignation is likely to disappoint investors.
It is likely they will want to see a credible and reliable replacement filling her shoes in order for them to continue investing in the country, says our correspondent.