Napout is said to have received bribes worth millions of dollars from broadcasting rights to the Copa America and Copa Libertadores tournaments.
The 57-year-old official must be collected by American authorities within 10 days.
”No details concerning when he will be handed over are to be disclosed for reasons of security and privacy,” the Swiss ministry said.
Napout was suspended from all soccer duty for 90 days by the FIFA ethics committee last Friday pending a full investigation.
Napout, who was elected in March, became the third straight head of the South American confederation – following Nicolas Leoz of Paraguay and Eugenio Figueredo of Uruguay – to be indicted.
Leoz is fighting extradition from his native country and Figueredo has been detained in a Zurich-area jail since May.
Napout was arrested Thursday ahead of attending a FIFA executive committee session which was to agree on anti-corruption reforms at the scandal-hit governing body. He faces a range of charges relating to racketeering, wire fraud and money laundering, and faces a 20-year sentence if convicted.
The multilingual Napout had seemed a part of FIFA’s future as it seeks to emerge from a corruption crisis.
”(Napout) sought to portray himself as an agent of reform, notwithstanding his own long-standing involvement in the solicitation and receipt of bribe and kickback payments in exchange for his influence as a CONMEBOL and FIFA official,” the U.S. indictment stated last Thursday.
Since May, Napout had become a key FIFA powerbroker and strong supporter of Michel Platini’s presidential bid before and immediately after his legal problems.
Napout then urged South America to switch support to another European candidate, Platini’s right-hand man at UEFA, general secretary Gianni Infantino.