The 48-year-old former striker inherits a side featuring mostly players born in the Netherlands and naturalised to represent the Southeast Asian nation.
"The Dutch football legend has signed a two-year contract from 2025 to 2027 with an option for an extension," Indonesia's football association, the PSSI, said in a statement.
Kluivert, whose managerial career has not matched his sparkling playing days, is scheduled to arrive in Indonesia on Saturday and will be introduced to the public the following day.
The Dutchman had been widely linked with the role after Indonesia controversially sacked the South Korean Shin Tae-yong on Monday.
Shin took Indonesia, who are 127th in the FIFA rankings, into the decisive third round of Asian qualifying for the 2026 World Cup in North America.
Indonesia have only been to the World Cup once, in 1938, when they were under Dutch colonial rule. The country gained independence in 1945.
They are firmly in the hunt for 2026, sitting third in their qualifying group after one win and three draws in six games.
The top two go straight to North America, with third and fourth going into another round of qualifying.
Indonesia's next qualifier is a crunch trip in March to Australia, who are second in Asian qualifying Group C but just a point ahead.
Japan are the runaway leaders of the group.
An Indonesian football association official admitted to AFP that Kluivert's appointment was not popular with fans, who were still behind Shin.
But the official, speaking on condition of anonymity, said: "Shin had communication problems with the European players.
"That's why the replacement is a Netherlands coach."
Amsterdam-born Kluivert retired as a player in 2008 after a stellar career that started at Ajax, where he won the Champions League, before moves to AC Milan and then Barcelona.
He was one of Europe's most feared forwards of his era, scoring 123 goals in six seasons for the Spanish giants.
He also scored 40 times in 79 games for his country.
Kluivert's managerial career has not been nearly as spectacular.
His last coaching role was in charge of Adana Demirspor in Turkey for five months in 2023.
Before that he was caretaker manager of Curacao in 2021.
Much of his coaching experience has been as an assistant, notably to fellow former Ajax and Netherlands player Clarence Seedorf with Cameroon in 2018-2019.
He was also number two to Louis van Gaal with the Dutch national side in 2012-2014.
