The defender arrives in a deal worth around £33million.
"We're delighted to welcome Benoit to Chelsea," Chelsea chairman Todd Boehly and co-controlling owner Behdad Eghbali said in a joint statement.
"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."
Badiashile, who has two caps for France, joined Monaco's youth team in 2016. The 21-year-old made 24 league appearances for Monaco as they finished third in the French league last season.
He will compete for the centre back position at Chelsea with the likes of Thiago Silva, Kalidou Koulibaly, Trevoh Chalobah and Wesley Fofana.
"I'm very happy to be here at Chelsea. I'm so excited to start playing for this club. I can't wait to see the fans and start playing in the best league in the world," Badiashile said.
Chelsea, who finished third in the league last season, are 10th ahead of facing Manchester City later on Thursday.