"I am sad to leave so many friends at Manchester United," Schweinsteiger told the club website (www.manutd.com).
"But I am grateful to the club for allowing me the chance to take up the challenge at Chicago Fire.
"I have enjoyed working with the manager, the players and staff here and wish them all the best in the future. But I have to reserve special thanks to the United fans -- whose support has been a very special part of my time in Manchester."
Fire's general manager Nelson Rodriguez believes the club are getting a proven winner in the former Germany midfielder, who must pass a medical and get a visa before joining.
HISTORIC MOMENT
"This is a historic moment for our club," Rodriguez said on the official Fire website (www.chicago-fire.com).
"Bastian’s talents, attitude, and character will be a perfect complement to our squad as we continue building a championship program."
Schweinsteiger spent 13 seasons with Bayern Munich before joining United, winning eight Bundesliga titles, seven German Cups and the Champions League in 2013.
He was also part of the 2014 World Cup-winning squad and represented his country 121 times before announcing his international retirement last July.
But he never got a chance under Mourinho, with Germany coach Joachim Loew saying Schweinsteiger could have helped United.
"I talked with him and he said he gave it everything in the past few months. There was some hope but for the longer term Manchester United were maybe planning without him," Loew told reporters on Tuesday ahead of Wednesday's friendly with England.
"It is a shame that it ended that way at Manchester. He could have helped them, in my opinion. He could have been their organiser in that midfield position."
Chicago have finished last overall in the MLS for the past two seasons.
(Reporting by Hardik Vyas in Bengaluru. Additional reporting by Karolos Grohmann; Editing by John O'Brien and Ken Ferris)
