The 20-year-old's contract expires on July 1 and has opted to sign for the Midlands club to link up with former Canaries boss Paul Lambert.
|11/2||Norwich are 11/2 with William Hill to finish in the top half next season
"Jed is an excellent young goalkeeper with a bright future ahead of him and was very much part of our plans for next season and beyond," he told the club's official website. "We offered him a good new contract but it looks like he has opted to sign for Aston Villa instead.
"We’re obviously disappointed to be losing the services of a very promising young England international goalkeeper and will be seeking substantial compensation from Villa."
Steer, who has represented England at Under-16, Under-17 and Under-19 level, has twice made first-team outings for Norwich and most recently spent a short time on loan at Cambridge United.