BlueCo, which owns both clubs in the deal, have moved quickly after they parted ways with Enzo Maresca on Thursday last week, bringing in Rosenior from the Ligue 1 club, where he has been successful.
In a statement, Rosenior said: "I am extremely humbled and honoured to be appointed Head Coach of Chelsea Football Club. This is a club with a unique spirit and a proud history of winning trophies.
"My job is to protect that identity and create a team that reflects these values in every game we play as we continue winning trophies. To be entrusted with this role means the world to me and I want to thank all involved for the opportunity and faith in undertaking this job. I will give everything to bring the success this club deserves.
"I believe deeply in teamwork, unity, togetherness and working for one another, and those values will be at the heart of everything we do. They will be the foundation of our success."
It has been a meteoric rise to the Premier League for the 41-year-old, who joined the French side in 2024 and led them to a seventh-placed finish, securing European football for the 2025/26 season.
He has also been crucial in their policy of playing young players, regularly starting games with 11 players under the age of 23, something that his new bosses at Chelsea will likely continue with.
Before then, he also had stints at Hull City and Derby County.
Rosenior becomes the fifth permanent head coach of Chelsea since the acquisition of BlueCo in May 2022, following in the footsteps of Thomas Tuchel, Graham Potter, Mauricio Pochettino and most recently, Maresca.
His first game in charge is likely to be their FA Cup game against Charlton on January 10th, with their midweek clash with West London rivals Fulham on Wednesday coming too soon for him.
Calum McFarland, who led the Blues to a 1-1 draw over Manchester City on Sunday, will be in charge for that game.