"It's official: Swiss authorities have agreed to Eugenio Figueredo's extradition to Uruguay," said Juan Gomez, lead prosecutor on the Uruguayan case.
"Swiss authorities will have until December 30 to complete the extradition."
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Figueredo, the former president of South American confederation CONMEBOL, was one of seven top football officials arrested in a raid on a Zurich luxury hotel in May, a raid that kicked off an unprecedented crisis at FIFA.
He has been indicted in the United States on charges of soliciting multi-million-dollar bribes from sports marketing firms.
But authorities in Uruguay launched their own investigation and subsequently charged him with abusing his office.
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Figueredo had agreed to be sent to Uruguay but was fighting extradition to the United States.
The Swiss justice ministry (FOJ) approved his extradition to both countries, and said in November it would be up to the United States to decide whether to let Uruguay have priority.
"If the US authorities do not agree, the issue will be decided by the FOJ," it said at the time.
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Gomez said last month that Uruguay would consider striking a deal with Figueredo, 83, if he cooperated with the investigation.
"The conditions for such a deal are that he reveal the identities of the perpetrators, co-perpetrators, accomplices or accessories after the fact who were involved," the prosecutor told local media.
Figueredo's lawyer Karen Pintos told AFP he was "willing to cooperate."
She also said she planned to request house arrest for her client due to poor health.
"He was ill before being detained, and it got worse in prison," she said.
The spiraling scandal at world football's governing body has led to the suspension of its president Sepp Blatter, who is currently answering to corruption allegations before FIFA's ethics committee.
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