Former Germany coach Klinsmann replaced Paulo Bento, who stepped down following South Korea's defeat by Brazil in the World Cup last 16 in December.
The Korea Football Association (KFA) said Klinsmann had signed a contract until the 2026 World Cup, which will be held in the United States, Canada and Mexico.
"I know that the Korean national team has been improving and achieving results over a long period of time," Klinsmann said in a statement.
"I am honoured to follow in the footsteps of the great coaches who have led the Korean national team, from Gus Hiddink to my predecessor, Paulo Bento.
"I look forward to doing my utmost to help the team achieve success at the upcoming Asian Cup and the 2026 World Cup."
After retiring as a player in 1998, Klinsmann was Germany head coach from 2004-06 and led them to a third-place finish at the 2006 World Cup on home soil.
He managed his former club Bayern Munich in the 2008-09 season before becoming head coach of the U.S. national team from 2011-16.
The 58-year-old led the U.S. to the CONCACAF Gold Cup title in 2013 and was named the CONCACAF Coach of the Year.
Klinsmann's first match in charge of South Korea will be a home friendly against Colombia on March 24th.
The KFA said Klinsmann's coaching team had not been finalised, adding that the German would live in South Korea for the duration of his tenure.
