The site at Ancient Olympia, 200 miles southwest of Athens, is normally off limits to such competitions and is used for the Olympic flame lighting ceremony.
The 15-country tournament will take place Saturday and Sunday.
Wrestling was one of the sports at the ancient Olympics, which also included running, boxing, long jump, javelin and discus.
"This was the birthplace of wrestling ... so we are going back to our roots," Nenad Lalovic, the head of the sport's governing body, said Friday. "We were very happy to be allowed to use a place like this for a wrestling tournament - and we're very thankful."
The IOC in February dropped wrestling from a list of core sports, leaving it to compete for a place in the 2020 Games against baseball and squash.
A decision will be made in September, when the IOC's executive board meets in Buenos Aires, Argentina, to select the host city for those Olympics.
Lalovic, a 55-year-old Serb, took over the federation after the sport's exclusion and said he hoped sweeping changes to the body's operating structure and new international competition rules would help get wrestling reinstated.
"We had a medieval constitution and we changed that," he said. "The Olympic Games are limited by the number of disciplines, and of course everyone who doesn't follow the instructions of the organizers must be punished. It's like having a very fast car and ignoring the speed limit."
The campaign to restore wrestling to the Olympics has received enthusiastic backing from Greek sports authorities and the conservative-led government, which agreed to host the weekend events despite steep cuts in public funding because of the country's financial crisis and international bailout.
"We are determined to offer every possible form of support to keep wrestling in Olympic competition," Yiannis Andrianos, a deputy minister for sport, said earlier this week. "It's an obligation we have both to modern Olympic history ... and in our roles as guardians of the heritage and spirit of the ancient games. Wrestling is a connection between the two."