The Canaries announced on Monday they had received a club-record fee for the 22-year-old, whose new deal ties him to Carlo Ancelotti’s side until 2025.
Godfrey made 30 appearances for relegated Norwich in the Premier League last season, and had been linked with a number of top-flight clubs during transfer window.
“It is an honour to sign for Everton and to be part of a huge club,” Godfrey told the club website. “”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 centre-back completed a medical with the Premier League leaders over the weekend.
He is Everton’s fifth signing of the summer after the arrivals of midfielders Allan and Abdoulaye Doucoure, playmaker James Rodriguez and left-back Niels Nkounkou.
Ancelotti’s team are top of the Premier League after winning all four of their opening matches.