The DR Congo midfielder has agreed a two-year contract and is City’s third summer signing following permanent deals for Tony Andreu and Graham Dorrans.
Mulumbu played 151 games in Albion colours during a six-and-a-half-year spell with the club, and Norwich boss Alex Neil told the club website: “The fact that we’ve been able to pick Youssouf up on a free transfer is a fantastic piece of business.
“His arrival will add to the competition for places. We have a strong squad with a lot of players that have done well in the Premier League and Youssouf will bring that competition to the squad.
“He has vast experience of the Premier League but he’s still at a good age. You generally say that a player comes into their peak between 27 and 32, and he’s right in the middle of that.
“He’s another fantastic player to add to an already-strong squad going into the Premier League.”