The 41-year-old Englishman is set to replace Enzo Maresca, who left on New Year's Day.
"I cannot turn down this opportunity to join an incredible club, incredible squad who are Club World Cup champions," Rosenior said.
Strasbourg are part of the Todd Boehly and Clearlake Capital-owned BlueCo multi-club ownership group that also controls Chelsea.
"I haven't signed yet. I have agreed verbally with Chelsea," Rosenior said.
"I will love this club for the rest of my life but I cannot turn down Chelsea."
Rosenior said Strasbourg first-team coach Kalifa Cisse, assistant head coach Justin Walker and head of analysis Ben Warner will also join Chelsea.
