Rosenior will take over duties from Enzo Maresca, who left Chelsea on New Year's Day on the back of a poor run which saw them win just one of their last seven Premier League games of 2025.
The Englishman was sacked by Hull City in the summer of 2024 after narrowly missing out on the Championship playoffs with a seventh-place finish, but replaced Patrick Viera at the helm of Strasbourg two months later.
The 41-year-old departs Strasbourg with the club in seventh place in Ligue 1, and heads for London with Chelsea's hierarchy getting increasingly agitated to not yet have ended their wait for a first Premier League title since 2017.
"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," Rosenior said.
"I am excited to work with this extremely talented group of players and staff, to build strong connections on and off the pitch, and to create an environment where everyone feels united and driven by the same goal.
"There is a real hunger to win, and I will give everything, every single day, to help this team compete and win at the very highest level to make everyone connected and proud to be a part of Chelsea Football Club.
"I want our fans to be proud of who we are and what we represent in every single game that we play. They are the soul of this enormous, historic and huge football club.
"I cannot wait to meet you all. I cannot wait to get started."
His first game in charge will be against London rivals Fulham on Wednesday, January 7th.