Switzerland`s Federal Office of Justice on Thursday said the requests were received July 1, within the 40-day deadline required.
They are based on a US federal probe into alleged bribery and racketeering worth more than $150m involving high-ranking officials at football`s world governing body.
All seven men, who - if convicted - face around 20 years in prison, have already objected to extradition.
They will be heard by Zurich police and granted a 14-day period to respond to federal officials about the extradition request, after which the Federal Office of Justice will rule on whether to extradite them. That ruling can be appealed to Switzerland`s top criminal court and supreme court.
The seven men, arrested May 27 in early-morning raids at a luxury Zurich hotel, include FIFA vice president Jeffrey Webb of the Cayman Islands and former FIFA vice president Eugenio Figueredo of Uruguay.
Costa Rican football federation president Eduardo Li was arrested two days before he was due to formally join FIFA`s executive committee.
Former Brazilian federation chief Jose Maria Marin led the 2014 World Cup local organising committee and is a member of the FIFA panel organising the Rio de Janeiro Olympics tournaments.
The others are Venezuela FA chief Rafael Esquivel; FIFA staffer Julio Rocha, a development officer from Nicaragua; and Costas Takkas, a Briton who works for CONCACAF President Webb.
The seven are among 14 indicted by the US Justice Department. Four more men have entered guilty pleas in the wide-ranging corruption case.
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