The Federal Office of Justice said the man, whom it did not identify, was extradited on Wednesday.
"He was handed over to a three-man U.S. police escort in Zurich who accompanied him on the flight to New York," the ministry said Thursday in a statement.
Reuters reported that a source told the new agency six days ago that FIFA vice president Jeffrey Webb of the Cayman Islands had agreed to be extradited.
The six other officials are fighting extradition.
The extradited man is accused of "accepting bribes totaling millions of dollars in connection with the sale of marketing rights to various sports marketing firms and keeping the money for himself," the Swiss justice office said last week.
All seven men were arrested on May 27 in dawn raids on a luxury hotel in Zurich by Swiss federal police at the request of American federal agencies.
They include Webb and former FIFA vice president Eugenio Figueredo of Uruguay. Both have been suspended from football duty by FIFA's ethics committee.
A total of 14 men — nine football officials and five marketing executives — were indicted by the U.S. Department of Justice in May, and a further four had their guilty pleas unsealed.
They are alleged to have taken part in a racketeering conspiracy paying bribes of more than $150 million over a 24-year period. The payments were tied to the award of broadcast and hosting rights for the World Cup, continental championships in North and South America, and regional club tournaments.
U.S. authorities have said more indictments should follow, and FIFA President Sepp Blatter is a target of the widening case.
Under pressure from the investigation, and a separate Swiss federal probe of money laundering linked to FIFA's award of 2018 and 2022 World Cup hosting rights, Blatter announced on June 2 that he would leave office within months.Suggest a correction