He was handed over to the US police in Zurich and then flown to New York.
Mr Li is one of seven officials with Fifa, world football's governing body, who were arrested in Zurich in May, amid a huge corruption investigation.
Separately, Switzerland will extradite former Fifa Vice-President Eugenio Figueredo to his native Uruguay.
In other developments:
Mr Li, a Costa Rican of Chinese origin, was extradited on a US arrest request, the Swiss authorities say.
He has been charged with conspiracy to racketeer, wire fraud conspiracy, wire fraud, conspiracy to launder money and money laundering.
He was elected to Fifa's executive committee - but was arrested two days before he was due to take up the post.
Mr Li was voted Personality of the Year 2014 in Costa Rica after the national football team stunned its rivals by reaching the quarter-finals in the 2014 World Cup in Brazil.
The Swiss justice ministry says Mr Figueredo - who is also a former vice-president of the South American Football Confederation (Conmebol) - was also detained in Zurich in May on a US arrest request.
Mr Figueredo has been indicted in the US on charges of receiving bribes worth millions of dollars relating to the Copa America tournament.
He is also accused of fraudulently obtaining US citizenship.
Switzerland says Mr Figueredo appealed against its September decision to transfer him to the US but later agreed to be extradited to Uruguay, where he is charged with abuse of office.
Until now, only one arrested official - former Fifa Vice-President Jeffrey Webb, from the Cayman Islands - has agreed to be moved from Switzerland.
At a hearing in June, Mr Webb pleaded not guilty to accepting bribes worth millions of dollars in connection with the sale of marketing rights.
He was placed under house arrest on $10m (Â£6.4m) bail by a New York judge.
What's in the Fifa indictment?
Who's been indicted?
Eduardo Li - former president of the Costa Rican Football Federation (Fedefut) - has been extradited to the US, the Swiss justice ministry says.