Kean joined the Canaries in July 2015 following his departure from Blackburn, but never played for the club.
The 25-year-old made a total of eight appearances in loan spells with Colchester and Swindon last season.
"There is a lot of competition but any competition is good competition," Kean told the club website.
"It's up to me to come here and have a go and try to get that number one shirt, but it's Keiren Westwood's at the minute and if I can provide more competition for him and make him play better, then great."
The length of Kean's deal at Hillsborough has not been disclosed.
Find all the latest football transfers on our dedicated page.
Championship side Sheffield Wednesday have signed goalkeeper Jake Kean after his contract with Norwich City was terminated by mutual consent.