The 32-year-old move is subject to a medical and a visa being obtained but Chicago are keen to finalise a swift transfer.
"I am sad to leave so many friends at Manchester United," said Schweinsteiger. "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.
"I was delighted to be part of the squad that won the FA Cup for them last season and will always remember their energy and their passion. Now is the right time for me to start a new chapter in Chicago and I am looking forward to it."
Everybody at United would like to wish Bastian the very best of luck in his new career in the United States.