Switzerland's Federal Office of Justice didn't identify the official involved, saying in a statement that he "wished not to be named at the moment."
The official, who initially had contested his extradition, agreed to be extradited on Thursday afternoon. The office said it approved his extradition immediately but that, in keeping with its usual practice, it would not give details of when he would be handed over.
Under Swiss law, he must be collected by a U.S. police escort and taken to the United States within 10 days.
The seven men arrested in raids on a luxury hotel May 27 in Zurich, where FIFA has its headquarters, included current and former members of FIFA's executive committee. The United States submitted a formal request for their extradition at the beginning of July.
The widening American investigation alleges bribery and racketeering worth more than $150 million involving high-ranking FIFA officials over a 24-year span.
The official who has agreed to be extradited is accused of accepting bribes totalling 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. Those rights were related to the broadcast of World Cup qualifiers, regional tournaments and continental championships in North and South America.