Godfrey, 22, completed his £25 million move from Carrow Road to Goodison Park on Monday morning, and will take on the jersey most recently occupied at Everton by goalkeeper Maarten Stekelenburg.
He previously wore the number four shirt both at Norwich, where he played primarily as a central defender, and at Shrewsbury Town, where he spent the 2017-18 season on loan from the Canaries in a defensive midfield role.
Following confirmation of his signing, Godfrey told Everton’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.”
Everton’s former number 22s include Steven Pienaar during his second spell at the club from 2012 to 2016, Aiyegbeni Yakubu from 2007 to 2011 and Tony Hibbert between 2004 and 2006.