Former Barcelona sporting director and player Cruyff, son of the legendary Johan, has been named technical adviser of the Indonesian FA.
The Indonesian football association (PSSI) in January appointed Netherlands and Barcelona great Kluivert as their new coach.
Indonesia are in the decisive third round of Asian qualifying for the 2026 World Cup in North America and have embarked on a recruitment drive of Dutch-born players, who will now be overseen by Dutch coaches.
Former Manchester United player Cruyff, 51, was chosen for his experience, which also includes managerial stints at Israel's Maccabi Tel Aviv and at Shenzhen FC in China, the PSSI said.
"His experience as a player and a coach will be crucial to build the future of Indonesian football," PSSI chairman Erick Thohir said in a statement.
Kluivert recommended his countryman for the role, Thohir said.
"I'm very excited. I can't wait to share my experience and knowledge to improve the level of Indonesian football," Cruyff said.
Indonesia are third in their World Cup qualifying group after one win and three draws in six games.
The top two go straight to North America, with the third and fourth going into another qualifying round.
The country's next qualifier is a crunch trip in March to Australia, who are second in qualifying Group C but just a point ahead, before a home fixture against Bahrain.