The World Cup winner sealed his switch to the United States after falling out of favour at Old Trafford under Jose Mourinho, failing to make a single Premier League appearance this season.
Nevertheless, Schweinsteiger reflected on a "great time" at United, insisting that he did not want his departure to overshadow the club's game against Middlesbrough prior to the international break.
"It was not easy as the decision was a little bit late so I did not get to say a proper goodbye team," he told the media as he was unveiled in Chicago on Wednesday.
"They had a match away on Sunday so I couldn't really tell them because I didn't want to have the focus on me. I wanted to have the focus on the team and on the game - I was very happy that they won.
"I had a great time there, especially with my team-mates and the staff there. I enjoyed it."
Chicago Fire (@ChicagoFire) March 29, 2017
Schweinsteiger says he opted to make the move to MLS as he sought a challenge that he believes he will get in Chicago.
"I like to challenge myself," the midfielder added. "This is a big chance to challenge myself. I know the results the last two years were not so good, but I can feel the vision.
"I can feel there is something going on and I want to help this club."