The 19-year-old made his first-team debut a year ago when Canaries boss Dean Smith was in charge at Villa Park.
"He's got great hunger and an urgency to learn and get better," Smith told the Norwich website.
"He's just on the back of winning the UEFA U19 tournament with England, so he's a confident boy and has played a couple of games for Villa in pre-season against Walsall and Leeds in Australia."
Ramsey is Norwich's fourth summer signing, following Isaac Hayden, Gabriel Sara and Marcelino Nunez.
"What I want to show the fans is that I can do things other people can't do, I can score goals and get assists - I just love creating goals," he said.
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