Following City's promotion to the Premier League, obligation to buy clauses in the deals for both Gibson and Giannoulis have now been triggered.
Norwich head coach Daniel Farke said: “We're very happy that both Dimitris and Ben are now permanent members of our squad.
"Ben has been great from the moment he walked through the door. His class and personality very much helped us stabilise our defensive behaviour. He's also a great leader and a fantastic person to have in the dressing room.
"With Dimitris, we were always fully convinced with his potential. He's in a great age and already has a lot of experience. He played for a big club in Greece and is a proven international player."