The sport's governing body selected Las Vegas over bids from several other cities including Tehran, New Delhi, Panama City, and Sochi, site of the 2014 Winter Olympics.
"Hosting the World Championships in Las Vegas is certainly a positive step forward in our quest to show the world the relevance of wrestling and help entrench our sport on the Olympic program," said Nenad Lalovic, acting president of the International Federation of Associated Wrestling Styles.
Wrestling was left in a state of shock last week after the International Olympic Committee made a recommendation last week to drop the sport from the 2020 Games.
Contested in the first modern Olympics in 1896 and part of the ancient Games in Olympia, wrestling joins baseball and softball, making a joint bid, martial arts karate and wushu, rollersports, wakeboarding and squash as candidate sports battling for one spot in a revamped program.
The IOC executive board will meet in St Petersburg in May to determine which of these will be put to the vote in September at the IOC session in Buenos Aires.