
The 26-year-old Frenchman, a defensive midfielder who can also play at centre back, becomes Norwich’s fifth arrival in the close season.
“I’m happy to play for Norwich… it’s a new challenge for me and I’d like to discover more about the Premier League,” Amadou told the club’s website.
“When I was young it was a dream to play in the Premier League, but the more I grew up, the more it became an objective. I had this opportunity right now and I’ve decided to take it. I will try to do my best in the Premier League.”
Amadou follows loan signings Patrick Roberts and Ralf Fahrmann into the club. Norwich have also completed permanent transfers for Josip Drmic and Sam Byram.
Norwich, who earned promotion to the top flight by winning the second-tier Championship, kick off their Premier League season with a trip to Liverpool on Friday.