The former Premier League player who is now 40 takes over from Frenchman Patrick Vieira, who left last week "by mutual agreement" with his name mentioned as a possible successor to axed USA coach Gregg Berhalter.
"His arrival will allow us to keep growing. He has a reputation for developing talent and we welcome him to the Alsace region," said Strasbourg president Marc Keller.
Rosenior played in the Premier League for Fulham, Reading, Hull and Brighton before retiring in 2018 to go into coaching.
He started as assistant to Wayne Rooney at Derby County before taking over from the former England forward on an interim basis.
From November 2022 to May this year he was in charge of Championship side Hull City.
Rosenior said he was delighted to be joining a club with such passionate support.
"I can't wait to get started," he said.
Strasbourg came 13th in the French top flight last season and play at Montpellier in their opener August 18th.
