The 20-year-old will link up with his new team-mates on July 1 when his Canaries contract expires and compete with Brad Guzan, Shay Given and Benji Siegrist for a starting berth
The 20-year-old will become the club's sixth summer addition when he links up with his team-mates on July 1 following the acquisitions of Jores Okore, Antonio Luna, Nicklas Helenius, Leandro Bacuna and Aleksandar Tonev.
|150/1||Aston Villa are 150/1 with Coral to finish in the top four next season
"Bringing in Jed will add to the goalkeeping department and helps with everybody pushing one another, learning from one another and making everyone better and wanting to improve," Lambert told the club's official website.
"You want competition for places throughout the team, which is something we didn't have last season."
Steer will compete with Brad Guzan, Shay Given and Benji Siegrist for a starting berth next season.