Formal extradition requests were submitted on July 1, the Swiss Federal Office of Justice (FOJ) said.
The seven top executives arrested in Zurich are among 14 FIFA officials indicted on charges of “rampant, systemic, and deep-rooted” corruption.
The charges follow a major inquiry by the FBI.
The FOJ said Zurich police, acting on its behalf, would give the seven officials a hearing over the extradition requests.
The officials and their lawyers would have 14 days to respond to the request, which could be extended, the FOJ statement said.
After that, the FOJ would give its decision “within a few weeks”, but warned that any ruling could be challenged in both the federal criminal court and the federal supreme court.
Jeffrey Webb, FIFA vice-president in charge of North and Central America, was among those arrested by Swiss police in a raid on a luxury hotel in the early hours of May 27.
The seven are among 14 defendants the US has charged with racketeering, wire fraud, and money laundering conspiracies.
In a 47-count indictment unveiled in a New York federal court, they were accused of taking part “in a 24-year scheme to enrich themselves through the corruption of international soccer”.
The indictment alleges that US and South American sports marketing executives paid and agreed to pay “well over $150 million” in bribes and other illegal payments to obtain lucrative media and marketing rights to football tournaments.
The corruption was planned in the US, the indictment said. The use of US banks to transfer money appears to have been key to the investigation.
The charges follow a three-year FBI investigation. It was initially sparked by the bidding process for the Russia 2018 and Qatar 2022 World Cups, but was then widened to look back at FIFA’s dealings over two decades.
FIFA President Sepp Blatter has not been indicted, although both the US and Swiss authorities have said they may interview him as part of their investigations.
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