The 22-year-old Englishman has moved to Goodison Park on a five-year contract worth £25m.
Godfrey is Everton’s fifth summer signing after Niels Nkounkou, Allan, Abdoulaye Doucoure and James Rodriguez.
Godfrey helped Norwich gain promotion to the Premier League two seasons ago but the Canaries suffered relegation last season. He played 30 times for Daniel Farke’s men in the previous campaign.
Godfrey told the club's official website: "It is an honour to sign for Everton and to be part of a huge club. I am very thankful for the opportunity and I can't wait to get started.
"The aim for me at Everton is to win trophies and win games. I like to win. I wear my heart on my sleeve. I care and I am a passionate lad.
"The fans can guarantee they will get 110 per cent out of me when I am on the pitch.
"This is a club full of history that has an exciting team full of world-class players who will help me kick on to the next level. I am looking forward to working with them and, hopefully, having great times with Everton Football Club.
"Carlo Ancelotti, Marcel Brands and the board want success for the club and it is really exciting to be here.
"The manager's past speaks for itself. He has worked with some top-class centre-backs. I will be able to learn so much from him and he is going to help me get to that next level, which is where I want to be."
Godfrey will have to wait until after the international break to make his Everton debut, with the Toffees locking horns with champions Liverpool on October 17.
