The 28-year-old England international began his career at York City before progressing through Norwich’s academy, where he became a key figure in their 2018/19 promotion to the Premier League.
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Godfrey later joined Everton in 2020 and made over 100 Premier League appearances during his time in England.
“I am buzzing, I am really happy to be here. I know the size of the club so it is a massive honour to be wearing the shirt this season, and I can’t wait to get started,” he told club website.
“I am looking forward to meeting the boys and hopefully helping this club achieve what it deserves, which is silverware and exciting times.”