The US has sought the extradition of the seven detained officials.
Swiss authorities have launched a separate probe into the decision to award Russia and Qatar respective World Cup hosting rights in 2018 and 2022.
Argentina great Diego Maradona, who has had a long-running feud with FIFA, praised the action of US and Swiss authorities.
"They called me mad, but thankfully today the truth is out and I am enjoying it," Maradona told Argentine radio station La Red.
"They hate football. They hate transparency. Enough shady dealings. Enough lying to the people."
Former Brazil striker Romario, now a federal senator, also applauded Wednesday's arrests.
"The imprisonment of Jose Maria Marin is the start of a great future for our football," Romario said in a televised statement.
"We hope that things change and that we can finally put people who act for the good of football in charge of its institutions."
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