The 20-year-old is set to join former Canaries boss Paul Lambert at the Midlands club when his contract expires on July 1. However, Norwich insist they will be seeking recompense for the development of the England youth international.
Norwich chief executive David McNally said on the club's official website: "Jed is an excellent young keeper with a bright future ahead of him and was very much part of our plans for next season and beyond."
He added: "We offered him a good new contract, but it looks like he has opted to sign for Aston Villa instead.
"We are obviously disappointed to be losing the services of a very promising young England international keeper and will be seeking substantial compensation from Villa."
Steer made 16 appearances for Norwich at senior level, and also had loan spells with Cambridge and Yeovil Town.
Lambert enjoyed a hugely successful spell as Norwich manager, taking the club to successive promotions back into the Barclays Premier League from npower League One.
However, the Scot then had a somewhat acrimonious departure at the end of the 2011-2012 season to take up the vacancy at Villa Park, with both Norwich and Lambert suing each other for breach of contract.
The matter was eventually settled before it was set to go to a Premier League tribunal.
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