Schweinsteiger, 32, joins on a one-year contract worth £70,000 a week, with the option to extend by a further 12 months.
Paunovic told Chicago Tribune: "We know it's going to take some time and adjustment for him coming to the new league, new coaching staff and everything.
"We also know we can rely on his capacity to adapt and do that fast."
He added: "He can produce actions that few players in the world can do.
“He sees [things] that nobody sees. He opens the eyes of the fans, where you can hear the people say, 'Wow!'"
Fire finished bottom of the league in the past two seasons.
The club's general manager, Nelson Rodriguez, said: “We're adding someone who has won at every level, including the very highest levels, and has done so in a way that is consistent with our values.
"Now we as a club need to rise to a standard that is set more internationally."