The president of FITA, Dr Ugur Erdener, made the announcement from the Federation’s headquarter in the Olympic Capital, Lausanne.
The announcement is the result of a bidding process that was launched in October 2007.
It follows Edinburgh staging earlier this year the World Cross Country Championships, hailed as the "best ever" by the International Association of Athletics Federations.
The event is set to be held in a city-centre location with Edinburgh Castle providing a stunning back-drop.
FITA, in cooperation with London-based company TSE Consulting, took the initiative in 2007 to make the World Cup Finals more attractive for potential hosts, athletes and spectators.
The event was formatted in a way that a city’s prime venue could be showcased to spectators and TV viewers during the event.
Erdener said: “The World Cup circuit continues to build recognition and attract both athletes and fans to the sport.
"With such strong and creative partners on board we have the platform to continue to build an even greater future for archery.”
Istanbul will host the event in 2011.
Steve Cardownie, Edinburgh's Deputy Leader and the city's festivals and events champion, said: "This is another huge honour for the city and underlines the high regard in which Edinburgh is held worldwide.
"We look forward to hosting the Archery World Cup in 2010 and I am certain it will be the best ever and a real attraction as we get closer to the Olympic Games in London."
Paul Bush, the chief operating Oofficer of EventScotland, the country’s national events agency, said: “We welcome the decision from the International Archery Federation to award Edinburgh the World Cup Final in 2010.
"With significant international TV and internet broadcast coverage, the event will provide us with a great opportunity to showcase Edinburgh and Scotland to a massive audience, and show that Scotland really does provide the perfect stage for events.”
Lynne Evans, chair of ArcheryGB, said: “Edinburgh is a fantastic Capital in which to stage the event, with its historic archery tradition and providing a fabulous backdrop to the modern image of our sport.
"This also automatically qualifies our archers for four places - one in each category - with a possibility of up to eight places in 2010."
The Archery World Cup consists of four stages held in spectacular venues around the world all culminating in a grand World Cup Final where only the top archers compete over two days.
This year’s World Cup Final will be held on September 27 In Lausanne following legs in Santo Domingo in the Dominican Republic, Porec in Croatia, Antalya in Turkey and Boe in France.