Badiashile will be with the Blues for seven and a half years.
Badiashile has played for Monaco in 135 league appearances.
The central defender, who made his senior debut for France in September against Austria, has joined Chelsea on a reported £35m deal.
I'm very pleased to be here. Badiashile is excited to begin playing for the club.
I am excited to start playing in the best league in the world.
The Frenchman has appeared in almost 150 games for Monaco, most of them in Europe's premier club competition.
Todd Boehly is the chairman of the Blues.
He is an excellent young player who has quickly established a strong reputation for himself and has a lot of experience for his young age. He will be a big part of our team in the future.
Graham Potter's side earned a point against Forest on Sunday and are currently sitting 10th in the league. The club are without defenders due to injury.
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