Both men have opposed their extradition to the United States at Zurich police hearings, Switzerland's justice ministry said in a statement.
Hours earlier, Swiss police made pre-dawn raids at the luxury Baur au Lac hotel in downtown Zurich, the same place where arrests on May 27 sparked the FIFA corruption crisis.
"According to the U.S. Arrest requests, they are suspected of accepting bribes of millions of dollars," the justice ministry said.
The bribes are linked to marketing rights for the Copa America, including the 2016 edition hosted in the United States, and World Cup qualifying matches.
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Napout, who is from Paraguay, is president of the South American confederation and Hawit, who is from Honduras, leads the North American regional body known as CONCACAF.
They are the third past or current presidents of each continental body to be indicted by the U.S. Department of Justice since May in a case that has shattered the reputations of soccer leaders in Latin America.
The reforms are a response to the dual American and Swiss federal investigations of corruption implicating FIFA leaders and which forced President Sepp Blatter to announce his resignation plans in June.
Fernando Sarney, a FIFA executive committee member from Brazil, said the arrests tainted what was intended to be a milestone day for the governing body to show it was committed to changing its culture.