According to the Associated Press, the official, who "wished not to be named at the moment," was one of seven arrested on May 27 when Swiss authorities raided the upscale Baur Au Lac hotel in the country's largest city, where FIFA has its headquarters, days before the 65th FIFA Congress.
The individual, who had initially contested the extradition, has been accused of accepting bribes related to the sale of broadcast rights for World Cup qualifiers, regional tournaments and continental championships in the Americas, according to Switzerland's Federal Office of Justice.
U.S. authorities now have 10 days, according to Swiss law, to collect the official for transport to the United States.
Fourteen people were charged by federal prosecutors in New York following a three-year investigation by the FBI that resulted in a 47-count indictment of current and former high-ranking officials including Jeffrey Webb, Eduardo Li, Julio Rocha, Costa Takkas, Jack Warner, Eugenio Figueredo, Rafael Esquivel, Jose Maria Marin, Nicolas Leoz and sports marketing executives Alejandro Burzaco, Aaron Davidson and Hugo and Mariano Jinkis.
The charges allege these officials were complicit in racketeering and bribery schemes involving more than $150 million going back more than 20 years.
FIFA President Sepp Blatter, who is also a target of the FBI investigation, was reelected in the days following the arrests but later announced his resignation.
Follow Matt Wilhalme on Twitter @mattwilhalme