Formal extradition requests were submitted on Wednesday, the Swiss Federal Office of Justice (FOJ) said.
The seven top Fifa 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 US Federal Bureau of Investigation.
The FOJ said Zurich police, acting on its behalf, would give the seven Fifa 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 “if sufficient grounds exist”, the FOJ statement said.
After that, the FOJ would give its decision “within a few weeks”, but that warned 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 seven top officials arrested by Swiss police in a raid on a luxury hotel in the early hours of 27 May.
They are currently being held in prisons around the Zurich region.
The suspects are among 14 defendants the US has charged with racketeering, wire fraud, and money laundering conspiracies.
In a 47-count indictment unveiled in a US federal court in New York, they were accused of participating “in a 24-year scheme to enrich themselves through the corruption of international soccer”.
Of the 14 charged, nine are Fifa officials and five are corporate executives.