Financial details were not disclosed but British media reported the deal was worth £35 million.
"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. He made 24 league appearances for Monaco as they finished third in the French league last season.
"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 in the standings after securing just one win in their last seven league games. They face second-placed Manchester City later on Thursday.
