Rosenior said Strasbourg first-team coach Kalifa Cisse, assistant head coach Justin Walker and head of analysis Ben Warner will join him at Chelsea.
Ronseior joined Strasbourg in July 2024 and guided the French club to seventh in Ligue 1 last season, securing European football for the first time in eight years.
His final match was a 1-1 draw at Nice on Saturday, their fifth league game without a win.
They are seventh in Ligue 1 and top of the Conference League.
“The last 18 months have been a joy and the best of my professional career,” Rosenior said.
“I’m here because I care about this club (Strasbourg) and I felt it was right to answer your questions physically here today before I move on.
“I will love this club for the rest of my life, but I cannot turn down Chelsea.”
Former Fulham and Hull defender Rosenior has never managed in the Premier League.
“I would not have accepted the Chelsea job if I was not ready,” he said.
“There are clubs you just cannot turn down. I hope the Strasbourg fans can see that and be proud of that.
“I have had interest from many clubs, including Champions League clubs, which I have always been open with to (Strasbourg president) Marc (Keller) and our ownership.”
Chelsea are fifth in the Premier League and face Fulham at Craven Cottage on Wednesday.
Caretaker manager Calum McFarlane took charge of the team for Sunday’s 1-1 draw at Manchester City.
