Formerly the assistant, Verbeek takes over from compatriot Dick Advocaat who stepped down after Korea were eliminated from the World Cup in Germany on Friday.
Earlier this month, Russia's Zenit St Petersburg said it would sign Advocaat as their coach after the World Cup.
South Korea's Football Association said Verbeek had signed a two-year contract.
The 50-year-old, who has 25 years' experience in coaching, played for Sparta Rotterdam from 1974-1980 and has coached Netherlands Antilles and Kyoto Purple Sanga in Japan's professional J-League.
South Korea bowed out of the World Cup after the first stage following a victory over Togo, a draw against France and a loss to Switzerland.
Despite the early exit in Germany, Advocaat won praise in South Korea for stabilising the team after his arrival in September.
Previous coaches Humberto Coelho and Jo Bonfrere were hounded from the job by a highly critical media and overly expectant fans.
Another Dutchman Guus Hiddink became a national hero in South Korea for taking the side on an improbable run to the semi-finals of the 2002 World Cup co-hosted by South Korea and Japan.
Verbeek was an assistant with Hiddink for South Korea during the 2002 World Cup.
"Verbeek has received offers to coach several professional and national teams, but he had a greater interest in the head coach job for the South Korean team, with which he has participated in two World Cup finals," KFA official Lee Young-moo told a news conference.
