The 25-year-old, who has moved to Carrow Road for an undisclosed fee, will now link up with the Scotland squad after penning a deal with the Canaries.
Hanley only made 10 Championship appearances for Newcastle last season, and has not featured under Rafael Benitez this term after falling down the pecking order.
Hanley told Norwich City TV: "Being able to come to a massive club and get games is a big motivation for me. It's a club with high aspirations and a fresh start for me. As a defender, I'm a bit of an old-fashioned no-nonsense centre-half and you pride yourself on clean sheets.
"We've got work to do on the training ground to improve that so I'm looking to hit the ground running. I can't wait to get started."
Norwich boss Daniel Farke added: "We're really pleased to sign Grant because it is clear our defensive line needs strengthening.
"He is a quality defender with very solid experience and is a leader too. I really like his attitude and his desire to come and play for us as well as the attributes he will add on the pitch."
Hanley played for Blackburn Rovers in the Championship between 2012 and 2016.