The U.S. Department of Justice issued an arrest warrant in May for Li, accusing him of taking bribes in connection with the sale of marketing rights for World Cup 2018 qualifying games.
Li, a Costa Rican citizen, was one of seven officials from world football's governing body taken into custody in a dawn raid on a luxury Zurich hotel on May 27.
He now has 30 days to appeal the decision, the Swiss Federal Office of Justice said in a statement on Tuesday.
Li will appeal the extradition, his Costa Rica-based lawyer Roger Guevara said in a statement to local media outlets. Li's U.S. lawyer declined to comment.
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Of the seven officials, former FIFA Vice President Jeffrey Webb agreed in July to be extradited to New York, where he has pleaded not guilty. The Swiss have also agreed to send Uruguayan citizen Eugenio Figueredo and Rafael Esquivel of Venezuela to the United States.
This group of seven are half of the 14 football officials and sports marketing executives indicted by the United States on bribery, money laundering and wire fraud charges involving more than $150 million in payments.
A parallel Swiss investigation into corruption in football widened last week to include FIFA President Sepp Blatter, who has denied wrongdoing.
(Reporting by John Miller and Joshua Franklin in Zurich; Additional reporting by Mica Rosenberg in New York and Enrique Andres Pretel in San Jose; Editing by Alison Williams, Bernard Orr)
