The Blues will pay up to £12.3 million to sign the 18-year-old, should all add-ons be met.
Real Madrid and Wolves had also shown interest in the American shot-stopper.
Slonina has penned a six-year contract with the Blues, but he will not link up with his new teammates until January 2023
“We're very proud and happy to see Gaga reach this milestone moment in his career," said Chicago Fire FC sporting director Georg Heitz in a statement.
“Since joining the club, Gaga has embodied what it means to be a Chicago Fire player. In addition to his incredible talent, he is mature beyond his years, extremely hard working and a fantastic teammate.
"Gaga is a role model to many young aspiring footballers in Chicago, and this transfer demonstrates that a player can progress to the first team from our academy before joining one of the biggest clubs in the world."
Welcome to Chels, @GabrielSlonina! pic.twitter.com/95F9qsCfhX
— Chelsea FC (@ChelseaFC) August 2, 2022