The 26-year-old allegedly came close to joining the Serie A side in January, but a move ultimately failed to materialise.
Ligue 1 outfit Lyon were understood to have tabled a £12.7m bid for Godfrey earlier this week, but the defender's preference was to sign for 2023-24 Europa League winners Atalanta, managed by Gian Piero Gasperini.
Godfrey moved to Everton from Norwich City for a fee rising to £25m in October 2020 and went on to make 93 first-team appearances across all competitions.
The versatile defender struggled for game time under manager Sean Dyche at the beginning of last season, but he established himself as a first-team regular during the latter stages of the campaign, starting 12 of the Toffees' final 17 Premier League matches.
Godfrey has now decided to make the move to Italy and becomes Atalanta's second signing of the summer transfer window after Charles De Ketelaere, who has joined permanently from AC Milan following a loan spell last season.
Godfrey, a two-cap England international, has taken to Instagram to thank Evertonians for their support during his four-year spell at Goodison Park.
"When I joined the club in 2020, everyone at the club from fans, staff and players made me feel welcome," a post from Godfrey read.
"I've made some great memories at this football club and will always appreciate my time there, and I feel like I can leave knowing I gave 100%. Now it's time to move onto my next challenge. Thank you for all your support. All the best Everton."
Reacting to his arrival at Atalanta, the defender said in a seperate post: My new home @atalantabc. So happy to be here, looking forward to meeting everyone at the club! Forza Atalanta!!!"
"Everyone at Everton thanks Ben for his service to the club and wishes him all the best for the future," said an Everton statement.
A statement from Atalanta read: "The Percassi and Pagliuca families and the whole club would like to extend a warm welcome to Benjamin Godfrey and wish him the best of luck in his future personal and team endeavours as a Nerazzurro."
Godfrey's departure from Everton will help boost the club's chances of complying with the Premier League's Profit and Sustainability Rules.