F1 chief Bernie Ecclestone had expressed doubts about whether the race could proceed, with a 21 September inspection called off.
In extending the time given to complete the track before the inspection, the FIA - motorsport's world governing body - had to stretch its own rules which said tracks should be given approval more than 90 days before the race takes place.
Whiting described the track as "satisfactory", adding that a license would be issued through the Korea Automobile Racing Association (KARA).
Local organizers had blamed bad weather for the delays in completing the Yeongam circuit, built on marshland near South Korea's south west coast and about four hours by car from Seoul.
The green light granted for Korea leaves three races remaining in the world championship this season. Red Bull's Mark Webber leads the standings by 14 points from team-mate Sebastian Vettel and Ferrari's Fernando Alonso.
Cranes are still in place in various areas around the circuit
KARA chairman Chung Yung-cho said: "We join the whole of Korea in welcoming the Formula 1 fraternity to the Korea International Circuit for the first time.
"We believe the 2010 Korean Grand Prix will be the catalyst to ignite enormous interest in the sport across the nation.
"The FIA has played a crucial role from the very beginning, and provided enormous support in terms of expertise, advice and knowledge."
He said the innovative layout of the circuit, bringing spectators close to the track while ensuring safety, had met with Whiting's approval.
No teams are expecting perfect conditions, however.
South Korea's car manufacturers hope the grand prix will help raise the country's image as a high-end maker, having emerged as one of the world's fastest growing exporters.
Cancellation would have dealt a major blow to South Korea's plan to raise its profile as a business and tourism destination.
Funds have been poured into various global events, including November's G20 summit and a bid to host the 2018 Winter Olympics.
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