The 21-year-old has cost Chelsea £35m and becomes their first major signing of the winter transfer window.
Badiashile has made 135 appearances for Monaco since breaking into the first team in 2018 and has been capped twice by the France national team, even though he was not part of their World Cup squad.
In a joint statement, chairman Boehly and co-controlling owner Behdad Eghbali said: "We're delighted to welcome Benoit to Chelsea.
"He's an excellent young player who has quickly established a strong reputation for himself and has a huge amount of experience for his young age. We are sure he will form an important part of our team in the years ahead."
"I'm very happy to be here at Chelsea. I'm so excited to start playing for this club," Badiashile said.
"I can't wait to see the fans and start playing in the best league in the world."
Badiashile could make his Chelsea debut against Manchester City in the FA Cup on Sunday.
"Benoit's growth over the last two-and-a-half seasons from a young player struggling to fully bring his talent to bear is testament to his and the staff's attitudes in adopting a higher professional standard," said Monaco sporting director Paul Mitchell.
"Signing with one of Europe's biggest clubs is the fruit of the work being accomplished within our academy and first team and once again highlights Monaco's ability to develop young players to the highest level."
