The 30-year-old made 31 appearances for the Canaries after arriving in 2012 and his arrival at Villa Park may pave the way for experienced keeper Shay Given to complete a switch to Stoke.
Bunn told Villa’s official website: “Aston Villa is a huge football club and this was too good an opportunity to miss out on.
“I’m looking forward to getting to know my new team-mates over in Portugal at our pre-season training camp and I can’t wait to get started.
“I’m delighted to find myself working with Tony Parks again, as he was the goalkeeping coach at Norwich City so he knows me really well.”
Bunn began his professional career at Northampton before joining Blackburn, and he has also spent time on loan with Leicester and Sheffield United.