It is understood Kean has penned a two-year contract with the Championship club, having had his contract terminated by mutual consent at Carrow Road.
The 25-year-old, who started his career at Derby County, joined Norwich last summer from Blackburn Rovers but failed to make a single appearance for the Canaries with John Ruddy and Declan Rudd ahead of him in the pecking order.
Keane said: “It’s been a strange year followed by a strange 24 hours with leaving Norwich and coming here but now I am just excited to be part of this squad and hopefully we can achieve something.”
Kean, who enjoyed loan spells at Colchester United and Swindon Town last season, has replaced Lewis Price, who opted to join Rotherham United last week.
Kean becomes Wednesday’s second summer signing and will provide cover and competition for Keiren Westwood, Joe Wildsmith and Cameron Dawson next season.