The 19-year-old has signed a contract at Carrow Road until the summer of 2024, but will spend the rest of the current season with his former club on loan.
Sitti has played 13 times in Ligue 2 so far this season, after making his professional debut for the club in July 2019.
He told the club's official website: "I'm very happy and glad to sign for this club. I'm so happy to be part of the Norwich City family.
"I chose Norwich because I love the way they play. I'm a big fan of the stadium as well.
"I have taken time to talk to my family and friends and I think it's the best choice for me to come here.
"In football, it's always difficult to change. But that's life and this choice is a positive one. I think I'm going to be very happy here."
Canaries manager Daniel Farke said: "Melvin is a very exciting player. he's young, talented and we believe he has real potential.
"He's had some very good experience of first-team football in France. We'll give him the time to further develop and an opportunity to impress.
"We're really looking forward to seeing how much further on Melvin can progress and we're all excited to welcome him to Norwich City."