The goalkeeper moves from Ewood Park to Carrow Road to provide competition for Canaries' first-choice, John Ruddy after deputising for Paul Robinson with Rovers
Bunn impressed both on loan at Sheffield United during the 2009-10 season and when deputising for Paul Robinson last season, keeping goal in Blackburn’s 3-2 win over Manchester United at Old Trafford.
The former Northampton goalkeeper has spoken of his delight at returning to the Premier League, and his excitement at working with his new team-mates.
"I’m delighted to be here to start a new challenge and I’m looking forward to it," Bunn told the club’s official website.
"I’m looking forward to seeing some familiar faces and getting to know the other lads. It’s a good time for Norwich – it will be a tough season and I think we’ll do well."
Bunn is also looking forward to reuniting with Canaries' goalkeeping coach Dave Watson, and hopes to improve as a goalkeeper under him.
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"I’ve come here as I want to challenge and I want to play and hopefully whoever is playing well will be in goal for Norwich."
Norwich boss Chris Hughton expects Bunn to provide experienced back-up for John Ruddy, and believes competition will benefit both goalkeepers.
"I'm delighted to have signed Mark," Said Hughton. "He is a keeper that will give us valuable experience and competition at first-team level."