The 41-year-old stated he was granted permission to speak with Chelsea and has verbally agreed to a contract, though it is not yet formally signed.
Rosenior described the move as an 'opportunity I cannot turn down', referring to Chelsea as 'one of the biggest sporting clubs in the world'.
His departure follows a successful period at Strasbourg, where he guided the club to seventh in Ligue 1 and the top spot in their Conference League group.