The Northern Ireland international has signed a five-year contract with Newcastle, who paid around £15m (€16.6m) for him.
Lewis, 22, was wanted by Liverpool boss Jurgen Klopp earlier this summer, a sign of his talent.
Despite Norwich’s relegation to the Championship last season, Lewis impressed and a transfer was just a matter of time.
Speaking to the club’s official channels after joining, Lewis said the move was unexpected, but exciting.
“It was a little bit unexpected,” he admitted. “But it was something that I was obviously looking forward to when I heard that there was serious interest, so I’m delighted to be here now.
“Newcastle’s such a great club with such history and I knew it was an opportunity I would love to take with both hands.”
Lewis follows Callum Wilson, Ryan Fraser and Jeff Hendrick into St James’ Park this summer.